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JOURNAL OF SEMANTICS Volume
12
Number 3
CONTENTS ALMERINDO E. OJEDA The Semantics of the Italian Double Plural
213
MICHEL AuaNAGUE
Orientation in French Spatial Expressions: Formal Representations and Inferences RENAAT DECLERCK AND ILSE DEPRAETERE
The Double System ofTense Forms Referring to Future Time
239
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The Semantics of the Italian Double Plural ALMERINDO E. OJEDA University ofCalifornia at Davis
Abstract The purpose of this paper is to endow the Italian double plural with a precise interpretation. Our main point will be that collective and distributive plurals denote algebras of the same type
semantically, a
homomorphic image
of its distributive counterpart.
If correct, these
interpretations will support the claim that nouns denote with a certain indeterminacy of indi
viduation (c£ Ojeda 1993a). They will also provide new evidence for the claim that the plural is semantically unmarked with respect to the singular (c£ McCawley 1968).
1 I NTRODUCT I O N Some masculine nouns ofltalian are said to have two plural forms. One of these forms is masculine and ends in i. The other is feminine and ends in -a. Semantically, many of the plurals in -a are said to have 'collective' force, while plurals in -i are instead said to be 'distributive' (Meyer-Liibke 1 905: §98), or 'singulative' (Regula &Jernej 1965: 87). Bur whar, exactly, do these terms mean? · Italian grammarians are seldom clear in this regard. 2 They simply tend to provide the reader with examples, glosses, or paraphrases of the plurals in question, perhaps adding that the plurals in -a have the collective value of the Latin neuters from which they ultimately derive (c£ Lausberg 1 962: §6o6; Rohlfs 1¢8: §368; Santangelo 198 1 ; 1 52). But no number of paraphrased examples can amount to a definition, and explanations in terms of the Latin collective would be satisfying only if we had a clear notion of the latter. Double plurals can be found in Italian which do not participate in an opposition of collectivity. We will discuss these plurals after interpreting the ones which do. We will then suggest how the meaning of each paired plural arises from the meanings of its morphological components. The claim will be that the difference between the two plurals is already present in their respective sterns. Hence the plural morphemes, which will be regarded as functors that are sensitive to the difference between algebras and subalgebras, will be able to combine with different kinds of sterns. Essentially, -i will combine with sterns which denote algebras while -a will combine with sterns which denote -
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and that, in certain cases, the algebra denoted by a collective plural is a subalgebra of the one
denoted by its distributive counterpart.• In such cases, the collective plural will be,
214
The Semantics of che Italian Double Plural
2
THE COLLECTIVE/DISTRIBUTIVE DISTINCTION
Let us begin with the case of ginocchio 'knee'. Ginocchio is a masculine noun which is said to have both a masculine plural ginocchi and a feminine plural ginocchia . Although many grammarians assert that there is little or no semantic difference between these plurals (c£ Battaglia & Pernicone 1978: 85; Fogarasi 1983: I96; Dardano & Trifone 1985: I I 8), not all specialists agree.To establish a semantic difference between the plurals in question, Rocchetti (I968: 357£) studied their use in I Racconti ofltalo Calvina (I958). He found that whenever knees were 'taken together' or 'used simultaneously for a same function', the form of choice was ginocchia ; when the knees were on the other hand 'dissociated' from each other, then ginocchi was used instead. Consider for example the cases in (I), which make reference to actions which involve knees jointly.3
( 1 ) a. Giovannino e Serenella ...si tenevano sull'orlo delle sedie, muovendo le ginocchia [37] 'Giovannino and Serenella were sitting at the edge of the chairs moving their knees' b. Si sedette tra noi sui divano ..., ci harte una mano sulle ginocchia [3 I 5) 'She sat between us on the sofa, patted us on our knees' c. il fatto d'aver [lei] alzato le ginocchia e accavallato le gambe [363] 'the fact of having raised her knees and crossed her legs'
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subalgebras.It will be seen that the semantic analysis we propose will allow us to eliminate the anomaly created, in Italian, by singulars having more than one plural. It should be noted that the contrast between plurals in -i and plurals in -a is not a productive one in Italian.Born of Latin neuter plurals by regularization and reanalysis, the contrast between plurals in -i and plurals in -a extended analogically to a number of nouns without neuter etyma (c£ Meyer-Liibke 1890: §§341 £).Yet, it did not extend to all Italian nouns.In fact, the contrast can be found only in a relatively small group of nouns. Furthermore, since the assignment of nouns to the neuter gender was to a large degree arbitrary in Latin, and since the domain of analogy is not predictable, the class of nouns for which the contrast holds does not form a natural class from a semantic point of view.In fact, there are many nouns in Italian referring to objects which tend to come collected in pairs or in groups (c£genitore 'parent', coniuge 'spouse', gemello 'twin', socio 'member/associate', etc.) but which do not avail themselves of the collective/distributive distinction. Given the history of this contrast, such gaps should not be surprising.
Almerindo E. Ojeda
21 s
d. [Ampelio] teneva soltanto i gomiti e le ginocchia sollevati in modo che i pugni di Quinto ... cadevano solo sulle braccia e sulle gambe [509] 'Ampelio only raised his elbows and knees so that the fists of Quinto fell only on his arms and legs' e. [egli] scendeva ... piegando le ginocchia e tenendo avanti le braccia [512] 'he was coming down bending his knees and extending his arms forward' In all these cases, ginocchia is used.There is also a case in whichginocchia is used when a group of knees is used to determine a unique height:
But ginocchia is mostly found in I Racconti when a pair of knees is used as a single resting point-in other words, when a pair of knees is used as a lap .4 (3) a. Era un grasso uomo . .. che .. . muoveva le mani su una carta topografica aperta sulle ginocchia [49] 'He was a fat man moving his hands on a map opened on his knees.' b. Io tenevo lo schioppo puntato appoggiato alle ginocchia [234] 'I had the pointed rifle resting on my knees' c. lei teneva Ia giacchetta sulle ginocchia [326] 'she had the jacket on her knees' d. ...stando seduto e continuando a leggere il libro che teneva sulle ginoc chia [370] 'sitting and continuing to read the book that he held on his knees' e. ... c'era anche un bambino sulle ginocchia d'una donna grassa (392] 'there was also a child on the knees of a fat woman' In fact, the only problematic use of ginocchia in I Racconti is (4), where there seems to be no reason for the two knees in question to constitute a unit. (4) Ia signora aveva ginocchia forti e grasse [322] 'the lady had strong and plump knees' The uses of ginocchi are straightforward.Consider the examples in (s), where the knees of a pair act independently of each ocher. (s) a. Erano accoccolati tutt'e due dietro le dalie, e i ginocchi rosa di Maria nunziata sfi.oravano quelli marrone tutti sbucciature di Libereso [2o] 'They were both squatting among the dahlias, and the pink knees of
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(2) E tutti costoro ...osservavano Federico steso li sotto all'altezza delle loro ginocchia [392] 'And all of them were watching Federico stretched out there at the height of their knees'
216
The Semantics of the Italian Double Plural
Maria-nunziata were barely touching the brown bruised ones of Libereso' b. . . . e il bassitalia li scavalco coi ginocchi per tornare al suo posto [1 1 1] 'and the Southerner pushed himself over them with his knees to return to his place' Or consider the examples in which each knee of a pair determines a distinct location, be it along a vertical dimension {6) or on a horizontal axis (7).5
But one of the most revealing uses ofginocchi arises when it occurs as the object of the preposition tra 'between'. For things can only lie between two points. To lie between two knees, the knees in question must therefore count as 'two' rather than 'one'. Since ginocchia views knees 'collectively', that is as 'one', only ginocchi is possible in this context: (8) a. Maria-nunziata . . . si stringeva Ia sottana era i ginocchi [24) 'Maria-nunziata was pressing her skirt between her knees' b. . . . il soldato . . . rannicchiato con Ia testa tra i ginocchi [6 3 ]. 'the soldier crouching with his head between his knees' c. Anche lei, a collo inclinato, con le mani tra iginocchi (262) 'Even her, with her neck bent, with her hands between her knees' As Rocchetti
(1968: 70) pointed out in relation to {8a), these sentences would simply make no sense with ginocchia . But I Racconti even provides us with minimal contrasts between ginocchia and ginocchi. They arise in situations in which hands are placed on knees. If the hands are placed one per knee (usually with the knees set apart) we have ginocchi:
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{6) a. [lei aveva) le calze di lana aiginocchi [236) 'she had wool socks to her knees' b. Sui tavoli c'erano donne che facevano danza . . . pure ognuno che allungasse una mano incontrava una natica o una mammella o una coscia che sembravano smarrite e non si vedeva di chi fossero: natiche a mezz'aria e mammelle all'altezza dei ginocchi [ 1 3 7] 'Women were dancing on the tables, and just anyone extending a hand would encounter a buttock, a breast, or a seemingly lost thigh, and one could not see whose it was: buttocks at midair and breasts at the height of the knees' (7) Ogni volta che si chinava Ia sottana le saliva piu su, scoprendo Ia pelle bianca dietro i ginocchi [24 7) 'Every time she stooped, her skirt would rise, exposing the white skin behind her knees'
Almerindo E. Ojeda 21 7
If, however, the hands are placed on the general knee region (usually with the knees next to each other), then ginocchia is preferred:
(10) a. Ora egli se ne restava con le mani sulle proprie ginocchia [327] 'Now he was with his hands on his own knees' b. Federico stette un po' li con le mani sulle ginocchia [393] 'Federico stayed there for a while with his hands on his knees'
3 A F ORMAL A C C O U NT O F T HE D I S T I N C T I O N To provide a precise account o f the semantics of the Italian double plural we will assume that an interpretation is always relative to a universe of discourse, and that a universe of discourse is a set on which a binary relation can be defined in a way which satisfies the following conditions of transitivity and completeness.
(I 1 )
TRANSITIVITY: If the binary relation holds between elements x and y of the universe of discourse, and between elements y and z of the universe of discourse, then the said relation also holds between elements x and z of the universe of discourse. (12) COMPLETENESS: Every nonempty subset of rhe universe of discourse constitutes one and only one element of rhe universe of discourse. 6
Intuitively, our assumption is rhat an interpretation always proceeds relative to a set whose elements are related as parts are related to wholes. We may therefore say x is part cify any rime we wish to convey rhe fact rhat the binary relation holds between some elements x and y of rhe universe of discourse. Furthermore, we may say that any element which is constituted by a subset of
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(9) a. . . . seduto su quegli sgabelletti da bottega, le lunghe mani Iisee da ladro sui ginocchi [ I 4 I ] 'sitting on those small shop stools, his long smooth hands of a thief on his knees' b. I1 posrino sogghignava, le mani sui ginocchi [ I so] 'The postman sneered, his hands on his knees' c. 11 pastore se ne stava guardando l'apparecchio con le mani aperte sui ginocchi [261] 'The shepherd was watching the machine with his hands opened on his knees' d. I due sedevano a poppa con le mani suiginocchi e sorridevano [338] 'The two men were sitting astern with their hands on their knees and smiling'
218 The Semantics of the Italian Double Plural
the universe of discourse is a group which has the elements of that subset as
members . It should be borne in mind, however, that nothing should be read into these uses of 'part', 'group', or 'member' chat does not follow from the mereological postulates of transitivity and completeness. Prima-facie evidence chat the relations between groups and their members
are indeed governed by the postulates in ( I I ) and ( I 2) is not difficult to produce.
ifthese things contain those, and ifthose things contain the things over there, then these things contain the things over there. The
Consider for example a sentence like
necessary truth of sentences like this one supports the claim chat the relation of inclusiveness between groups is transitive. Or consider the fact chat any group of things, be it finite or infn i ite, may be referred to-say by phrases like
those
or simply the things.This fact argues for the claim that the universe of discourse is closed with respect to the operation of group formation underlying the notion of constiruency, and therefore satisfies completeness in the sense of(12)J Having availed ourselves of the foregoing assumptions and definitions, we may now claim that ginocchi denotes the set of arbitrary groups of knees of the universe of discourse while ginocchia denotes the set of natural groups of knees of the universe of discourse-the set of pairs of knees of each individual and the group formed by these pairs. To illustrate, let us say that the universe of discourse contains only four knees a , b , c, d.This means that the universe of discourse will contain fifteen groups of knees (one per nonempty set of knees).These groups are listed in ( I 3), where a and
a + b is the group having a and b as members, a + c is the group having c as members-and so on.
a , b, c, d , a + b , a + c, a + d, b + c, b + d, c+ d, a + b + c, a + b + d, a+ c + d, b + c+ d, a+ b + c + d
( 13)
a , b, c, d as groups of knees.This is forced on us by (12) and the fact that {aj, (bJ, {cj, {dj are all nonempty subsets of Notice that we regard the individual knees
the universe of discourse. But the groups in( I 3) are related as parts are related to wholes, with a +
b+
c + d being the single most inclusive group, and a , b, c, d the four least inclusive groups.These relations impose a partial order on the elements of ( I 3).
The Hasse diagram of this order is given in ( I 4). This diagram contains an upward path from a group xto a groupy if and only if xis part ofy (andy is not part of x).
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things, these things ,
Almerindo E. Ojeda 2 1 9
B+b+C+d
�
a+b+c a+b+d
b
b+C+d
c
d
We may now diagram the denotations ofginocchi and ginocchia in this universe of discourse. Let us suppose that our universe of discourse contains two people, and that a and b are the knees of one of them while c and d are the knees of the other. The masculine ginocchi will then denote the entire set of groups of knees of (r3):
=
[ginocchi ]
The feminine ginocchia, on the other hand, will only denote the set of groups of pairs ofknees in the universe of discourse, as indicated in (16). 8
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a
B+C+d
220 The Semantics of the Italian Double Plural
(r6)
S+b+C+d
=
a
b
c
[ ginocchia]
d
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Incidentally, notice that ginocchia can be used to refer either to the pair of knees of a single individual or to the pairs of knees of several individuals. The first use can be found in ( rc-e), in (3), and in (4); the second in (r a-b) and (2). This means that [ginocchia] should contain both individuals (- individual pairs of knees) and groups (- groups of pairs of knees). The use of ginocchia thus provides further evidence for the claim that plurals are semantically unmarked with respect to number. 9 Plurals denote without prejudice against singularity; they are neutral with respect to the difference between the one and the many. We have argued that ginocchi denotes the set of groups of knees of a universe of discourse while ginocchia denotes the set of natural groups of knees of a universe of discourse. [ginocchia ] is thus contained as a subset in [ginocchi ]. In fact, [ginocchia ] is moreover embedded as a subalgebra in [ginocchi ], as we shall now see. Take any set of groups of knees contained in [ginocchi]. By ( r 2) this set will itselfconstitute a group ofknees. But this group must again be contained in [ginocchi ], since this is the set of all the groups of knees in the universe of discourse. The set denoted by ginocchi is therefore closed under mereological group formation.10 Now, let k be the group constituted by all the knees in the universe of discourse. Take any group of knees other than k. Call this group g. Find all the groups of knees which do not share any knee with g . There will be exactly one of these groups which will constitute k with g. This group is the mereological complement ofg with respect to k .11 But this complement is itself a group of knees. It will therefore be contained in [gino cchi] since, again, this is the set of all the groups of knees in the universe of discourse. The set denoted by ginocchi is therefore closed under mereological complement formation. 12 The set denoted by ginocchi is therefore closed under mereological group formation as well as under mereological complement formation (with respect to the group of knees of the universe of discourse). Since it lacks a null element, it is thus a mereology in its own right.13 Let us now turn to ginocchia . We have argued that it denotes the set of groups of pairs of knees of a universe of
Almerindo E. Ojeda 221
4 THE C O LLE C T IVE/D I S T RI BU T IVE D I ST I N C T I O N : M O RE I N STA N C E S Similar interpretations are available for other nouns referring to objects which come naturally in pairs. On the feminine plurals of these nouns, 'a dual meaning is imposed, more or less by force, by the physical structure of the things they refer to' (c£ Hall I9 s 6: I40). Some ofthese nouns refer to body parts. Consider, for example, the case of sopracciglio 'eyebrow'. Its feminine plural sopracciglia is used when the two eyebrows count as one-as in (I7a), where the two eyebrows describe a single line. The masculine sopraccigli, however, is used when the two eyebrows count as two-as in (I7b), where two eyebrows approach each other (c£ Rocchetti I968: 70; Brunet I985: 73). (17) a. [Cassola] Aveva la faccia larga, con gli zigomi appiattiti, e la linea delle sopracciglia un po' obliqua '( S]he had a long face, with cheek-bones leveled and a somewhat oblique eyebrow line' b. [Manzoni] e allora due sopraccigli neri si ravvicinavano, con un rapido movimento 'and then two black eyebrows approached each other with a fast movement'
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discourse. Take now any set ofgroups of pairs ofknees contained in [ginocchia]. By (I2) this set will itself constitute a group of kneepairs. But this group must again be contained in [ginocchia] since this is, we have claimed, the set of all the groups ofkneepairs in the universe of discourse. The set denoted by ginocchia is therefore closed under mereological group formation. Now let p be the group constituted by all the kneepairs in the universe of discourse. Take any group ofkneepairs other than p. Call this group q. Find all the groups of kneepairs which do not share any knee with q. There will be exactly one of these groups which will constitute p with q. This group is the mereological complement of q with respect top. But this complement is itself a group of kneepairs-at least if all the knees in the universe of discourse are paired. It will therefore be contained in [ginocchia] since this is the set of all the groups ofkneepairs in the universe of discourse. The set denoted by ginocchia is therefore closed under mereological complement formation with respect to p. We have shown that the set denoted by ginocchia is closed under both group and complement formation. [ginocchia] is, therefore, a mereology in its own right. In fact, it can be shown that [ginocchia] is a subset of[ginocchi] which is closed under group and complement formation as taken in [ginocchi]. This means that [ginocchia] is a submereology of[ginocchi].14 Ginocchia thus denotes, as claimed above, a subalgebra embedded in the algebra denoted by ginocchi.
2.2.2.
The Semantics of the Italian Double Plural
Also claimed to belong in this class is calcagno 'heel'. Its masculine plural is calcagni, and is said to refer to 'heels in general', while its feminine plural calcagna is supposed to refer to 'the two heels [of each individual]' (Jordan & Manoliu 1974: 280).51 But not all plurals in -a need involve paired body parts. Corna 'horns' may refer to the horns of the moon, the horns of an anvil, or the branches of a river forking in two-at least when regarded collectively; when regarded singularly, then the masculine corni would be used instead {c£ Goidanich I967: I42).16 Similarly, the noun lenzuolo 'bed sheet' has a masculine plural lenzuoli and a feminine plurall en zuo la . The masculine lenzuoli is used when a 'multitude' of sheets is taken 'one by one', as in
The feminine lenzuola is used when sheets are taken by pairs corresponding to beds-i.e. the top and the bottom sheet of a bed (c£ Battaglia I98I: I Io; Dardano & Trifone 1985: I IS; Brunet I98s).This may happen either with a single pair of sheets (I9a), or with a set of pairs of sheets (I9b): {I9) a. [Pasolini] Piano piano, come guidato da quella musichetta lontana, esce dalle lenzuola, si cala dal lettino . . . 'Little by little, as i f guided by that distant music, [s]he leaves the sheets, climbs down from the couch .. .' b. Voglio due paia de lenzuola 'I want two pairs of sheets' interesting use of lenzuoli is given in (2o). Although this sentence involves reference to the two sheets of a bed, the adjective doppia 'double' and the preposition tra 'between' require us to regard these sheets as two rather than as one. The form lenzuoli is thus the appropriate one in chis context.17
An
(2o) [Moravia] Tarcisio la vide ... mettere un ginocchio sul letto e ingolfarsi, bruna, tra la doppia bianchezza dei lenzuoli 'Tarcisio saw her put a knee on the bed and plunge, tan, between the double whiteness of the sheets' Similarly, one says lenzuolifunebri 'burial sheets' or avvisi come lenzuoli 'signs [big] as sheets' because the sheets in question 'are not considered paired' (Goidanich I967: I4J). For all these double plurals, if all the individual knees, eyebrows, heels, horns, and sheers are paired, then each feminine form will denote a submereol ogy of the mereology denoted by its masculine counterpart. So suppose chat we could map each group in the denotation of a masculine plural into a unique
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{18) [Salvalaggio] Mafalda stendeva i lenzuoli sul terrazino 'Mafalda was hanging the sheets on the balcony'
Almerindo E. Ojeda 223
Le braccia
son membri del corpo 'The arms are limbs of the body' (22) [Pavese] A vedergli le membra muscolose poco piu che ventenni, Stefano pensava con invidia al nero sangue che doveva nutrirle ... 'Seeing his musculous limbs little more than twenty years old, Stefano thought with envy of the black blood which must have nourished them'
(21)
What is more, according to some grammarians, the collective/distributive opposition between membra and membri holds even when these plurals are used figuratively to refer to the metaphorical limbs of a metaphorical body. Thus, countering the claims of other grammarians, Goidanich (1967: 140, 143) has documented a number of figurative uses of membra (c£ when Gioberti conceives of the Christian peoples as le membra della Chiesa 'the limbs of the Church'; when Dante speaks of the particular sciences as le membradellafilosofia 'the branches (lit. limbs) ofPhilosophy'), and alleged that there is a collective/ distributive contrast between them and their masculine counterparts. Along the same lines, Devoto and Oli (1971) have mentioned the figurative use of membra in raccogliere le sparse membra di un popolo 'collect the scattered membership (lit. limbs) of a population'. Here they find a plural 'from the elements of which a human community or aggregate results' (c£ Brunet 1985: 64)· There are other examples of plurals in -a which do not involve pairs. Consider the noun osso 'bone'. The plural ossa refers collectively to bones-be they the bones of a single skeleton (23a), the bones of many skeletons (23b) or, as
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group of pairs which contains it minimally.This mapping would be a homo morphism from the denotation of the masculine plural onto that of the feminine.18 Intuitively, this homomorphism compresses the denotation of a masculine plural into that of its feminine counterpart; the denotations of masculine and the feminine plurals are 'telescoped' versions of each other. But plurals in -a need not even involve pairs. Suppose there were a human who developed three legs (and hence three knees). As one of the anonymous reviewers for this article pointed out, we can still describe his anatomy by reference to le tre ginocchia 'the three knees'. Fortunately, our proposals are compatible with this fact, as all we require is that the denotation ofginocchia be based on groups of individual knees; we do not require it to be based on actual pairs of individual knees. Consider also the singular noun membro 'limb' has a masculine plural mem bri and a feminine plural membra. The masculine membri is reserved for limbs referred to 'singularly', as in (21), where two of the four limbs of the human body are referred to. The feminine membra is preferred for limbs referred to 'collectively', as in (22), where all the limbs of a body are described as a whole (c£ Devoto & Oli 1971).
224 The Semantics of the Italian Double Plural
Brunet (1985: 71) pointed out, the bones of particular bone structures like that of the foot (23c), the face (23d), or the chest (23e).
The plural ossi, on the other hand, refers distributively to bones 'considered separately', to bones 'separated from each other, without regard to their totality' (c£ D'Ovidio & Meyer-Liibke 1906: 161; Rohlfs 1968: 36; Battaglia 1981: I 11; Fogarasi 1983: 195; Brunet 1985 : 70): (24) a. gli ossi del lesso, d'una bistecca; gli ossi sparsi per la via 'the bones of the boiled meat, of a steak'; 'the bones strewn on the street' b. (Silane) Le bandiere . . . erano nere . . . e avevano nel centro l'immagine d'un teschio tra quattro ossi 'The flags were black, and had in the middle an effigy of a skull among four bones' c. [Pratolini) gli ossi gli bucavano la carniciola . . . 'the bones perforating his vest . . .' Similar distinctions have been claimed for the plurals of muro 'wall' and dito 'finger/toe'. Mura 'walls' refers to walls of enclosure (2sa}-(25b), walls that define a perimeter (25c), and hence an interior (2sd}-(25e), and an exterior (2sf). (25) a. (Cassola] . . . avanzo della medioevale cinta di mura 'ruins of the medieval town walls'
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(23) a. (Cassola] Aveva donnito pochissimo, e si sentiva la testa pesante e le ossa rotte '[S]he had slept very little, and felt his/her head was heavy and his/her bones were broken' b. [Levi] 11 paese e fatto delle ossa dei morti 'The country is made of the bones of the dead' c. [Palumbi] in virru di questa tipica disposizione ad arco delle sue ossa, il piede puo agevolemente sostenere tutto il peso del corpo 'By virtue of this typically arched disposition of its bones, the foot can easily support all the weight of the body' d. [Carriere della Sera] L'allineamento dei denti e lo sviluppo delle ossa della faccia dei bambini non preoccupava . . . 'The alignment of the teeth and the development of the bones of the face of the children did not trouble . . .' e. [Carnacina-Veronelli) Con un colpo deciso della mana sui coltello spezzare le ossa del petto e ritirarle 'With a firm blow ofthe hand on the knife, break the bones of the chest and take them out'
Almerindo E. Ojeda 225
The masculine muri, on the other hand, may refer to arbitrary collections of walls-say the walls that were damaged in some incident (26a), the walls on which signs are posted (26b), the walls which divide a space (26c), or the pairs of walls enclosing a street (26d), or, figuratively, a period of time (26e). See Goidanich (I967: I44), Santangelo (I98I: I I 7), and Brunet (I98 s: 66 f£). (26) a. Sono lesionati due muri 'Two walls were damaged' b. attaccare avvisi ai muri 'to post signs on the walls' c. muri divisori 'dividing walls' d. [Papini] Di sopra ai muri in cui Ia strada era incassata si spenzolavano i rami convulsionari de' bigi ulivi 'Over the top of the walls in which the street was encased hung the convulsed branches of the grey olive trees' e. [Ottieri] ...Ia domenica fra due muri, che sono Ia settimana a riddosso e quella futura ... '...Sunday between two walls, which are the week gone by and the one to come . . .' Similarly, the singular noun dito 'finger/toe' also has a masculine plural diti and a feminine plural dita. The masculine diti refers to fingers or toes taken 'one by one' (c£ Fogarasi I983: I9)), 'considered distinctively one from the other' (Dardano & Trifone I985: 1 18).The feminine dita, on the other hand, denotes
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b. [Moravia] c'e un cimitero di campagna, piccolo, con quattro mura chiuse intorno un mazzo di cipressi 'it is a country cemetery-small, with four walls closed around a bunch of cypresses' c. [Bassani] via Salinguerra sia compressa ... dentro il perimetro delle mura cittadine 'Salinguerra street is contained ... within the perimeter of the city walls' d. [Essere donne in Sicilia] il potere femminile e stato sempre esercitato dentro le mura domestiche 'Feminine power has always been exercised within the domestic walls' e. [Moravia] Tra queste quattro mura Maria Teresa andava e veniva 'Within these four walls, Maria Teresa went to and fro'19 £ [Moravia] erano andati a stare in una casa nuova, situata fuori delle mura della citra 'They had gone to stay in a new house situated outside the walls of the city'
226 The Semantics of the Italian Double Plural
-
s
OTHER DISTINCTIONS EXPRESSE D BY THE DOUBLE PLURAL
But it should be acknowledged that not all the double plurals ofltalian exhibit a collective/distributive contrasr, some exhibit a count/mass contrast instead.22 Perhaps the clearest instance of such a contrast can be found in connection with the plurals of cervello 'brain'. Its masculine plural cervelli 'brains' is a count noun (c£ due cervelli d'agnello 'two lamb brains', i cervelli piufini della nazione 'the finest brains in the nation') while its feminine plural cervella 'brain mass' is a mass noun (c£ cervellaJritte 'fried brains , fars i saltare le cervella 'to blow one's brains out'). To be more precise we will propose that cervelli denotes an atomistic mereology (the set of groups which are constiruted by one or more of the '
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the fingers or toes 'considered as a whole' (Dardano & Trifone 1985: r r8; Fochi 1971: 147).Thus we have questi due diti mifanno male 'these two fingers hurt me' but le dita della mano 'the fingers of the hand' (Battaglia & Pernicone 1978: 84).20 And again, if all the individual limbs, bones, walls, and fingers/toes are suitably grouped in a universe of discourse, then the feminine plurals membra, ossa, mura, and dita will denote submereologies of the mereologies denoted by their masculine counterparts. We conclude, then, that the collective/ distributive distinction exhibited by the Italian double plural is one of submereological inclusion-at least in those universes of discourse in which all the relevant individuals are appropriately grouped. 21 At this point we should mention the interesting fact that paio 'pair' does not have the plural in -i generally available to masculine nouns.Rather, it has only a plural in -a. It should be clear that this fact is consistent with the analysis of the double plural presented in this paper.For suppose that the singular paio denotes not a set of individuals, but only a set of pairs of individuals (of the universe of discourse). It can hardly be surprising, in light of the above, that this noun would then allow only a plural in -a and not a plural in -i. Of course, since the present proposals do not ensure that a plural in a will be available for any particular noun (and since, as we shall see, -i does not moreover select for improper submereologies), the foregoing analysis does not properly predict this gap in the paradigm of paio. Still, it can describe it. We close this section by pointing out that (17a), (19a), (22), (23 a, c, e), and (25) are plurals which make reference to an individual pair of eyebrows, an individual pair of sheets, an individual group of limbs, several individual bone groups, and a number of individual wall enclosures.All these plurals thus refer without prejudice against individuality-as one would expect if the plural is indeed the semantically unmarked member of the opposition of number.
Almerindo E. Ojeda 227
(27) (Palumbi] II carpo (della mano] consta di 8 ossa brevi disposte in duplice fila 'The carpus of the hand is composed of eight short bones arranged in double file' Furthermore, plurals in -a, unlike mass nouns, may denote clearly shaped entities-recall/a linea delle sopracciglia in ( I 7a) and il perimetro delle mura cittadine in (2sc). Yet there does seem to be something to the claim that plurals in -a tend not to be enumerated. After all, the plurals in -i have been characterized as 'numerical' in opposition to the collective plurals in -a (cf Goidanich 1¢7: 14o ff). As we see it, the collectives' intolerance of enumeration should be accounted for in terms of a conflict between collective and enumeration: collectivity is the view of many as one; enumeration is the recognition of one as
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individual brains of the universe of discourse) while cervella denotes an atomless mereology instead (the set of portions of the infinitely divisible brain mass in the universe of discourse).23 Note that this means that the plurality of the mass noun cervella can only pertain to form, not to meaning (plural nouns refer to groups of indivisibles, of which a mass noun has none).The plurality on cervella is thus as devoid of meaning as the pluralities on the English mass nouns oats and news. To find more examples of double plurals which participate in a count/mass opposition we must leave contemporary Italian. For indeed, although grammarians are far from agreed on this subject, it would seem thatjrutto 'fruit' and legno 'log' used to have two plurals each.One was a count noun ending in -i; the other a mass noun ending in -a .24 Now this situation has all but disappeared. Today the plural instances of Jrutta and legna have become rare and restricted in their use (Brunet 1985: 87, 90)-if not relegated only to prescriptive grammars (Rocchetti 1968: 87). Furthermore, the mass nouns in -a have been reanalyzed as singulars (Fochi 1971: 148 £; Sensini 1988: r66) without any discernible change in their meaning (Rocchetti 1968: 67). The latter, of course, should not be surprising. As we have seen above, the plurality on these mass nouns was semantically vacuous in the first place. The role of the count/mass opposition has been overplayed in the context of the Italian double plural.It has been argued, for example, that the plurals in -a are all mass nouns since they may not combine with numerals (cf Renzi 1988: 326). The claim, however, is questionable, not only because of the way these plurals have been paraphrased in the literature but, more importantly, because the grounds for the claim are simply not there. Plurals in -a may indeed combine with numerals.Examples of this have been given above in due paia di lenzuola (r9b), con quattro mura chiuse (25b), and tra queste quattro mura (25e). Another counterexample can be found in (27), cited in Brunet (1985: 70).
228
The Semantics of the Italian Double Plural
(28) a. (Buzzatti) Gia carnminavo de mezz'ora per quei budelli ... 'I had walked for half an hour through those streets .. .' b. Da questa piazzetta a quella s'arriva per un groviglio di budelli scuri e sudici 'One gets from this small square to that one through a tangle of dark and dirty streets' Similarly, of the two plurals of fondamento 'foundation', the feminine Jondamenta refers to the foundations of a house or edifice ({ondamenta di un edificio ), while the masculine Jondamenti refers to the foundations of a science (fondamenti di una scienza) or a state (fondamenti di uno stato) . Analogous distinctions can perhaps be drawn for the plurals of labbro 'lip', ciglio 'eyelash', andfi lo 'thread' (c£ Goidanich I967: I4I f£; Battaglia & Pernicone I978: 84; Fogarasi I983: I95). Needless to say, the algebraic account proposed in the preceding section will not apply in these cases.Yet it would be interesting to determine whether that account obtained at earlier stages of the language. One should note in this regard that Santangelo (I98I: 105 £) finds two nonfigurative uses of bracci in her survey of Old Italian texts. One of these is l'un de' bracci 'one of [her] arms' (Decameron VII.2.J2), where a distributive plural is used, as one would expect, in a partitive construction (to refer to one of her arms, the arms in question must count as a 'many' rather than as a 'one').Similarly, Santangelo (I98I: II4) finds a clear collective/distributive contrast in giungi i labri a le Iabra join the lips to the lips' Uerusalem Liberated r 8.J2). Nonfigurative uses of bracci seem to have survived also in the Tuscan vernacular (c£ Goidanich I967: I4I), the dialect which in general seems to preserve best the plural endings in -a (c£ Fochi I97I: 146). Grammarians have also claimed that some double plurals participate in a container/content opposition.The plurals of carro 'can' are thus said to be carri 'carts' and carra 'carts with their contents' (c£ Rohlfs IJ&malllits
©Oxford Uniwrsiry Pn-ss 1 995
1 2: Z JI)-267
Orientation in French Spatial Representations and Inferences
Expressions:
Formal
M I C HEL AU RNAGUE Equipe de Recherche en Syntaxe et Semantique-CNRS, Universite de Toulouse-Le Mirail
Abstract
1 INTRO DUCTION This work on orientation 1 comes within the framework of research in spatial semantics developed over the past ten years both in cognitive linguistics (Bierwich & Lang 1989; Herskovits 1986; Lang 1990; Talmy 1983; Vandeloise 1986a) and computational semantics (Habel 1987; Pribbenow 1993). 1t is part of a broader project which aims at giving a formal representation of the semantic content of French linguistic markers of space (Barilla, M. 1991).In the category of referents, this project has dealt with Internal Localization Nouns (henceforth ILN) such as haut (top), avant (front), intirieur (inside), bord (edge) which are all lexical elements pointing to the different portions of an object. As for spatial relations, we examined internal and external prepositions (sur (on), dans (in)! devant (in front of ), au-dess us de (above), etc.) as well as several verbs of motion (se diriger vers (to go towards), venirde (to come from), passer par (to go through)).
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In this paper we propose several formal tools intended to grasp an important aspect of static localization in language, namely orientation. We consider French spatial expressions used in localizing an entity in an internal way (Internal Localization Nouns such as haut (top), bas (bortom), devant (front), derriere (back)) or in an external way (prepositions devant (in front of), derriere (behind), au-dessus de (above), au-dessous de (below)). In order to represent these orientation phenomena, we build a logical framework made up of three levels that we call geometrical, functional, and pragmatic. First, we define a geomerry based on directions and relative localization operators. Then we inrroduce the functional notions that underly intrinsic orientation processes and we propose several formal definitions which may serve to represent the semantic content of the srudied lexemes. These definitions allow us to make a difference between deictic and intrinsic uses of these spatial expressions and to draw interesting deductions and inferences. Finally, we integrate at the pragmatic level various principles governing the interpretation of such orientationa! expressions. By taking into account the dif ferent inferential schemata linked to the use of spatial expressions in discourse, this modular approach constirutes an original contribution to the semantic and cognitive srudies of linguistic space.
240 Orientation in French Spatial Expressions
2 A THREE -LEVEL SYSTE M F OR THE RE PRESENT ATION O F S P ACE IN L AN GU A GE This section is a summary of what is presented in Aurnague & Vieu (1993). Contrary to Leech (1969) and to a certain extent to Miller & Johnson-Laird (1976), several linguists showed that a purely geometrical representation of the semantics of spatial prepositions is not appropriate (Herskovits 1986; Lang 1990; Talmy 1983; Vandeloise 1986a). For instance, if sur (on) was represented only in terms of contact, we could not differentiate between the sentences:
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A semantic analysis of these lexemes highlighted some important properties of spatial structures in language {Asher & Sablayrolles 1995; Aurnague 1989; Aurnague & Vieu 1993; Borillo, A. 1988, 1992;Laur 1991).On the basis of these observations, a formal system of representation of spatial entities and relations was proposed which consists of three levels encoding geometrical, functional, and pragmatic data. Orientation does in fact play a great part in the semantics of most of these ILNs as well as in the semantics of prepositions such as sur (on), au-dessus de (above), derriere (behind), etc. (that is to say, in both referent and relation categories and in both internal and external cases). We present in this paper a formal treatment of orientation which improves various aspects of a previous formalization we gave in (Aurnague 1991 and Aurnague & Vieu 1993) to represent this important feature of spatial semantics.This new formal tool tries to grasp better the differences between deictic and intrinsic orientation, and it can be used to handle both internal and external localization ( le haul (the top}/ au-dessus de (above), /'avant (the front}!devant (in front of ), etc.). Here we follow the methodological choices that were defined for the whole research project Firstly, from an empirical point of view, the study has been based on a detailed and systematic linguistic analysis which must highlight and classify the different meanings of each lexeme, in particular the distinct spatial configurations it refers to. The second point addresses the elaborated formalisms which, beyond the representation of the semantic content, should have adequate inferential properries.More precisely, we want to be able to use the formal representations we build in order to draw inferences whose results have to be in accordance with the results of natural reasoning made by human beings. In this paper, we will first recall the main characteristics of the overall representation system of the semantics of spatial expressions already proposed and focus on the orientational part. We will then introduce new tools for dealing with orientation in internal and external localization processes.
Michel Aurnague 241
La tapisserie est sur le mur (The wallpaper is on the wall) L'armoire est contre le mur (The cupboard is against the wall)
2.1
The geometrical /eve/
At the geometrical level, we deal with the topological notions of inclusion, contact, boundary, etc., and with concepts related to projective geometry such as straight line, distance, order on a straight line, etc. At this level, we deal with the spatial referents of the entities, that is, the space portions determined by their matter at a precise moment. These elements are also called here individuals. The actual use of prepositions like sur (on) and dans (in) which allow us to
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In this example, the geometrical approach does not take into account the functional component of the semantics of the preposition sur (on) corres ponding to the notion of'support'. More generally, the functional aspects of the relations and entities involved in spatial expressions play a major part in the semantics of spatial markers. However, we do not claim, as Vandeloise does, that functional notions alone can fully explain spatial semantics and we think that geometrical and functional data need to be articulated. As in any field of natural language, pragmatic phenomena influence the semantics of spatial markers. For instance, a book is usualy said to be on the table, even though the book is on another book and thus not in contact with the table. Because the relation between the two books is not relevant, one can 'forget' about it and think of the book directly in relation to the table. In Herskovits ( 1 986), Herskovits shows that, if instead of two books one on top of the other, it was a lid on a teapot, it would be impossible to 'infer' that the lid is on the table. In this case, being on the teapot, the lid fulflls its function with respect to the teapot and this fact cannot be 'forgotten'. Several pragmatic principles can be isolated which are in fact instances of more general ones governing any kind of discourse or dialogue such as Grice's principles of cooperativity (Grice 1 975). For instance, the underlying pragmatic principles involved in the previous example are the maxims of relevance and quantity. If a fact is relevant (in this case the lid is on the pot), expressing a less precise fact (in this case the lid is on the table) somehow implies that the precise fact is not verified in the given situation. According to these remarks and to several others of the same kind, we have proposed to analyse and represent the meaning of spatial expressions by means of a three-level system which takes into account geometrical, functional, and pragmatic information.
242 Oriemarion in French Spatial Expressions
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situate an entity called 'trajector' with respect to another entity called 'landmark' shows the relational nature of the structures handled in language, as opposed to the absolute spaces used in robotics (where entities are localized by means of coordinates). Moreover, two properties of these absolute spaces seem to contradict the structures of space in natural language. Whereas in a coordinate system the positions of every entity need to be known exactly, the spatial information expressed in a text is often partial and imprecise. Another problem arises from the fact that the variable granularity of space in language (for instance, the same entity can be considered at one time as a point and later as a volume) is not compatible with the discrete structure characterizing an implementable coordinate system, where the minimum units are defined a priori. So knowledge representation at the geometrical level will be achieved through a relational structure rather than through a coordinate system. Consequently, the spatial referent of the entities will be viewed as primitive elements and not, for instance, as sets of points within a Euclidean space. Space is therefore built from the text and not assumed beforehand (this is similar to the construction of time proposed in Kamp ( 1979)). In order to reflect these characteristics of linguistic space, topological data are represented in our system by means of Clarke's individual calculus (Clarke 1981, 1 985; Randell & Cohn 1989) which we modified and completed so as to take into account some important spatial concepts in language. This calculus, which is based on the sole primitive relation of connection between two individuals (C(x, y)), is used to define some mereological, as well as Boolean and topological, operators. As regards mereology, we can mention inclusion, overlapping, and external connection between two individuals. In the Boolean part of the calculus, operators such as sum, product, and complement are introduced. As for topological aspects, the interior of an individual, its closure, and the properties of being closed and open can be defined. Individual calculus based on connection is not sufficient as it is to deal with some problems related to the semantics of space in language. Consequently, we extended this theory to express some fundamental spatial notions such as limits and contact. We introduced three types of limit relations (lim 1 , lim2, lim3) through which surface-, line-, or point-like individuals can be differentiated. These limit concepts are very important for the formalization of ILNs like dessus {top extremity), bord (edge), angle (comer), etc. (Aumague 1 991 ). We also added the strong contact notion represented by external connection (the individuals in contact are assumed to share part of their boundaries) a notion of weak contact (the individuals are not connected although they touch) which seems to match common sense better. Let us suggest that contact plays a big role in the semantics of the relation sur (on). At a second stage, spatial points are constructed as sets of individuals by a
Michel Aurnague 243
2.2
Thefunctional level
At this level, we deal with properties linked to the entities themselves and therefore we handle variables representing entities and not mere pieces of space. We use the 'function' strej (spatio-temporal referent) in order to associate an entity with the spatio-temporal individual it determines throughout its 'life'.2 One of the most important processes which takes place on the functional level concerns orientation. In the same way as we retricted the type of entity processed by the system, we introduce some constraints on orientations. First, the texts studied are 'instantaneous' in the sense that the entities described as well as the speaker do not change positions with respect to one another.
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method akin to the maximal filters construction for defining time instants in a theory of time based on events or periods (Kamp 1 979; van Benthem 1 98 3). To avoid inconsistencies, the construction of 'interior points' (the individuals of these points overlap two by two) needs to be differentiated from the construc tion of 'boundary points' (there are two externally connected individuals in these points); this is one essential aspect of our modification of Clarke's theory (Vieu 1 99 1 a). Having built the 'points' and introduced two new primitive relations between points 'is situated between' noted T and 'is closer to' noted K (adapted from van Benthem 1 98 3), we define the notions of straight line (maximal set of points satisfying three by three the relation 'is situated between'), equidistance, perpendiculars (two lines are perpendicular if in each line there exist two points such that the two points of one line are equidistant to each point of the other), parallels, etc. As already mentioned, at the geometrical level, not only do we take into account topological data, but we also integrate some imponant concepts from projective geometry. We associate a system of abstract (not oriented) axes and directions with the spatial referent of every entity and we locate the different portions with respect to the whole entity by 'projecting' them on these axes. It should be made clear that an important assumption of our study is based on the delimitations of the universe of spatial entities that we describe and process (essentially with respect to their shape). For the analysis of ILNs, we had to restrict the research field of spatial entities to solid, undeformable, and connected objects that also have a 'normal usefulness'. This is why we deal here with a class of individuals whose shape is roughly parallelepipedic, cylindrical, or spherical. However, we think that these methodological restrictions are quite reasonable because the mental encoding of the entities involved in spatial relations seems to call for a very simple specification of their shape (Landau & Jackendoff 1 993; Talmy 1 98 3). We can conclude the presentation of this level by saying that we obtained a complete relational geometry.
244 Orientation in French Spatial Expressions
2. 3
The pragmatic level
Some pragmatic principles act on the semantics obtained at the previous levels in a significant way. On top of functional knowledge, they use world knowledge (in particular, knowledge of typical situations) and information about context. The principles we consider here may be seen as the instanciation of more general ones (such as Gricean cooperativity principles (Grice 1975)) in the spatial domain. First, pragmatic principles allow one to deduce, in some cases, more information than is really present in the text and is represented on the first two levels (so we need a non-monotonic logic on this level). For instance, the sentence Marie est dam Ia voiture (Mary is in the car) is generally understood as Mary is in the passenger space, discarding at the same time the alternative Mary is in the boot. Second, they may rule out some expressions (for example, expressions inferred at the previous levels) because, even though their 'crude' semantics is verified by the system and in the model, they cannot be uttered since, using the first process mentioned, these expressions would be regarded as conveying information contradictory with what is known. For instance, if we know that
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Moreover, we assume that an entity is oriented by a single speaker. As stated before, only abstract directions are handled in the geometrical module. The orientation process, which is greatly conditioned by functional features, consists in mapping an abstract orientation on to a concrete one. Apart from the notion of orientation, we introduce at the functional level some concepts belonging to 'naive physics' (Hayes 1985) such as support and containment. As shown in the beginning of section 2, support is essential in sur s semantics: an object hanging above a table, touching it, is not sur Ia table (on the table). Containment which plays a great part in the determination of natural inside can be described as the restriction to some potential movements of the content. At this level, we distinguish three types of entities: objects (as in all the examples above), locations (countries, cities, gardens . . .), and non-material 'space portions' (such as insides of objects, holes, cracks . . .). Using those categories and a lattice structure for representing plural entities, we define six types of part-whole relations which play a great part in some uses of dans (in) (Vieu 1991a, 199 1 b). Thanks to these tools, we introduce some formal definitions for the lexemes we study, that is to say, for ten ILNs as well as for the prepositions sur (on) and dam (in). According to our methodological choices, we check whether the definitions we give in our system allow inferences in accordance with natural 'deductions'.
Michel Aurnague 245
2.4
Focus on orientation
Let us go back to the way the orientational process was defined in the formal system we have presented up to now. We said that the spatial referent of every entity is linked to a system of abstract orthogonal axes; as we will see, this is not a very accurate representation of what really takes place. In fact, a detailed study of orientation shows that an intrinsic orientation follows from the internal properties of an entity, in particular its shape but also its function (Bierwisch & Lang 1989; Lang 1990; Vandeloise 1986b). Con sequently, the axes or straight lines arising in such an intrinsic orientation are linked to the entity itself and not just to its spatial referent. This is the case of a TV or a house which both have intrinsic vertical and formal orientations. Intrinsically oriented entities can be classified according to the way this orientation arises. For example, Bierwisch & Lang ( 1989) introduces a sub categorization of vertical intrinsic orientation into three classes. In that analysis, fixed orientation occurs when entities have a fixed orientation with respect to the earth's surface (mountains, rivers), whereas canonical orientation applies to situations calling for a normal position with respect to the vertical (TVs, desks), and inherent orientation occurs when vertical orientation comes from inherent properties of the entity (books, pictures). In the case of a contextual process, orientation is the result of the interaction between the entity involved and another entity in the context This means that the relevant axes in a contextual orientation derive from the interaction between these two entities. For instance, such an orientation occurs when one designates the front of a tree situated in front of a tent (in this case, the front part of the tree is the part which faces the entrance of the tent). In the framework of this study, we only consider a particular case of contextual orientation, namely
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Marie estdans le cojfre de Ia voiture = Mary is in the car's boot is true, then Marie est dans Ia voiture = Mary is in the car is not false, and yet in general we cannot answer where is Mary? with the latter sentence, for in most contexts it is interpreted as Mary is in the passenger space. A 'fixation principle' underlies the examples cited above. This principle, first introduced in Vandeloise (1986a), expresses the fact that the typical use of an object 'fixes' some of its characteristics. For instance, the front and the back of a car are 'fixed' by the usual-not the actual-direction of its motion; indeed, many intrinsic orientations are determined this way. Several other principles may be found. Third, we must mention the pragmatic phenomenon that enables us to loosen some conditions of the semantic definitions. This phenomenon was illustrated in the previous example of the books on the table which involved the maxim of relevance.
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Orientation in French Spatial Expressions
3
A N A LY S I S A N D F O RMAL I ZAT I O N O F O R I E N T AT I O NAL P R O CE S S
Having presented the main characteristics o f our system for the representation of spatial entities and relations, we are now going to describe the new tools we
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the deictic one, in which the orientating entity is the speaker. However, interpretations relying on vertical contextual orientation (which is given by gravity) will be formalized because, very often, vertical deictic uses are restricted to situations where the speaker is standing up. So ifwe wanted to give a very accurate account of the orientational process as it really occurs, we would have to associate predefined axes only to intrinsically oriented entities, whereas for a deictic orientation the axes would be defined by taking into account the interaction between the oriented entity and the speaker. However, this is not the case in the formalism already proposed, even though we could determine whether we are faced with a deictic or intrinsic case. First, and as we indicated above, every entity has (at the geometrical level) a predefined system of abstract axes associated with it. Second, although the formalism mentions elements which entail the association of an abstract direc tion with a concrete one (in an intrinsic case this process is triggered by the entity itself, whereas in the deictic one it relies on another element of the context, the speaker), this complex functional process is not described in details for each case.3 According to these remarks, our new orientation formalism has to fulfil two main points. First of all, it has to grasp how the axes derive from the function of the entities and the shape of their spatial referents. Concerning chis point, it can be underlined that giving an intrinsic orientation to an entity in a determined direction amounts to saying that for 'functional reasons' a particular portion of this entity constitutes an extremity in this direction (e.g. usually the neck of a bottle is up). A second requirement for the new formalism relies on the need to use the same orientational tool for internal ILNs, as well as for external localizations (e.g. devant (in front of), derriere (behind), au-dessus de (above), au-dess ous de (below)).4 The main reason for such a requirement is that, from an inferential point of view, we want to be able to combine formal definitions of external and internal markers and to derive calculations from these combinations. Another reason would be that, from linguistic and psychological points of view, the orientational mechanisms involved in internal and external localization seem to be very similar.
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introduce in order to deal with orientation. We will detail the formalisms operating at each level of the system. 3.1
The geometrical level
A1 V a , {3 (PT( a ) 1\ PT(f3 ) 1\ --.ND(a , {3)) => 3D d(a , {3) = D Henceforth, directions will be denoted by upper case characters so as to differentiate them from individuals and entities which are noted in lower case. Another axiom indicates that symmetrically ordered pairs of points determine opposed directions (the opposite operator '-' being defined below (Defi )): A2 V a , f3 (Pt(a ) 1\ Pt(/3 )) => (d(a , {3) = D d(/3 , a ) = -D) We introduce a primitive relation between directions Kd(D 1, D2, D3) which expresses that 'D 1 is closer to D2 than to D3' (in terms of angular values). Such a relation, similar to the primitive K expressing relative distance between points (axiomatized in van Benthem 198 3), is irreflexive and transitive (and thus asymmetric): A3 VDI , D2 --.Kd(DI, D2, D2)
A4 VD 1, D2, D3 (Kd(D 1, D2, D3) 1\ Kd(D 1 , D3, D4)) => Kd(D 1, D2, D4) As in the case of the primitive K between points, a second type of transitivity can be stated:
As VD1, D2, D3 (Kd(D1 , D2, n3) " Kd(D3, D1, D2)) => Kd(D2, D1, D3) The primitive relation Kd allows us to characterize the notions of opposite and orthogonal directions. The opposite of a direction is the direction which is the farthest from it, whereas a direction orthogonal to a given one is situated at an equal distance from this direction and its opposite (this last notion is defined in a set theoretical way):
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At the geometrical level we complete our ontology by introducing the basic concept of direction. Directions have already been used in various works in the field of Qualitative Physics (Davis 1989; Frank 1 992; Freksa 1993) or in semantic studies intended, for example, to handle the spatial information contained in car accident reports Gayez 1 992). A direction is viewed here as a primitive element which can be linked to ordered pairs of points by the following axiom, d( a , {3) being a new primitive function giving the direction determined by two points a and {3 and ND a relation expressing the notion of null distance (Aumague & Vieu 1 993):
248 Orientation in French Spatial Expressions
Defi -(D I , D2) =def VD3 D3 � D2 � Kd(D1 , D3, D2) Def2 Ortho(D1) - def (D2: -D I - D3 1\ --.Kd(D2, D1, D3) 1\ --.Kd(D2, D3, D1)) Let us indicate that a particular axiom ensures the existence of the opposite of any direction: A6 \fD1 3 D2(VD3 D3 ¥ D2 � Kd(D1, D3, D2)).
Def3 Med(D1 , D2) -der {D3: {D I - D2 A D3 - D1) V (D 1 � D2 1\ -.Kd(DJ, DI, D2) A --.Kd(DJ, 02, DI))} Def4 VDI , D2, D3 D3 E Sum(D1 , D2) (D3 E Med(D1 , D2) A VD4(D4 E Med(D1 , D2) => -.Kd(DI , D4, D3))) A7 VDI , D2, DJ{DI � D2 1\ D I � 03 A D2 � D3) => (Kd(DI , D2, D3) v Kd(D1, D3, D2) V D 1 E Med(D2, D3)) By means of the following two axioms we express the reflection or circular aspect of directions: AS \fD1 , D2, D3, Kd(D1 , D2, D3) () Kd(D 1 , -03, -02) A9 \fD1 , D2, D3 Kd(D1 , D2, D3) () Kd(-DI , -02, -03) Finally, we state a kind of transitivity between medians and we express the relation of a direction D with respect to two directions D2 and D3 in terms of the sum of these directions: A10 VD, D1, D2, D3 (D E Med(D1, D2) 1\ D E Med(D2, D3) 1\ D 1 D E Med(D1 , D3) AI 1 VD, D 1 , D2, D3{Kd(D, D2, D3) 1\ D1 E Sum(D2, D3)) � {Kd(D3, D1, D) 1\ Kd(-02, -D I, D))
� D3) �
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From A6 and the fact that the opposite of a direction is unique (which can be proved using A6 and asymmetry), it follows that the relation '-' can be characterized as a function. Consequently, we will use the operator '-' as a function rather than as a simple relation, -D denoting the opposite direction of a direction D. We can also define the median of two directions and a kind of sum or composite of directions. The median of two distinct directions correspond to the set of directions which are equidistant between these two directions. The sum of two directions is a subset of the median set constituted by the directions which are the nearest from these two directions (this set is a singleton for non opposed directions and its element corresponds to the median which is coplanar with the two directions, whereas for opposed directions it has for two elements in 2D space and it corresponds to a whole plane in 3D space). We give below the set theoretical definition characterizing medians and sums as well as a linearity axiom:
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The theory based on this primitive Kd includes other definitions and axioms concerning, among other things, extensionality and coplanar directions. Although these notions should be of great importance for a complete geometry on orientation, we do not introduce them here because they are not relevant to the semantics of the spatial relations we are dealing with in this paper. Several theorems can be proved from the set of definitions and axioms set out below, in particular with regard to orthogonality:5
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A3 A4 A7 A8 Defi TI \fDI , D2, DI � D2 � Kd(-DI , D2, DI) For every direction D2 different from D I , -D I is closer to D2 than to D I A3 A4 Defi TI T2 \fD -(-D) = D Idempotency of T3 \fD, DI, D2, D3 D I e Med(D2, D3) 1\ Kd(DI , D2, D) � A4 A7 Aw Def2 Kd(DI , D3, D) If D I is the median of D2 and D3 and DI is closer to D2 than to D it follows that D I is closer to D 3 than to D T4 \fDI, D2, D3 DI e Med(D2, D3) 1\ D I e Ortho(D2) � D I e Ortho(D3) A8 A10 Def2 Def3 T2 T3 If DI is the median of D2 and D3 and DI is orthogonal to D2 then DI is orthogonal to D 3 A9 Def2 Ts \fDI , D2, DI e Ortho(D2) -DI e Ortho(D2) Saying that DI is orthogonal to D2 is equivalent to saying that -DI IS orthogonal to D2 T6 \fD, D I (DI e Ortho(D) � \fD2(Kd(D, D2, -D2) Kd(D, D2, DI))) A3 A4 As A7 AS Def2 Def3 T2 T4 Ts IfDI is orthogonal to D, saying that D is closer to D2 than to -D2 is equivalent to saying that D is closer to D2 than to D I T7 \fDI, D2, Kd(DI , D2, -D2) Kd(D2, D I , -DI} A3 A4 A7 AI I Def2 Def3 Def4 T6 Saying that D I is closer to D2 than to -D2 is equivalent to saying that D2 is closer to DI than to -DI T8 \fDI , D2, DI e Ortho(D2) D2 e Ortho(DI) Symmetry of orthogonality A more complete presentation of this theory on orientations detailing the different deductions which can be drawn will be proposed in Asher, Aurnague, & Vieu (forthcoming). Let us indicate that this axiomatic needs to be studied further in order to minimize the number of axioms and to verify its properties from a model theoretical point ofview (in particular, soundness). To formalize correctly the orientational process, we also have to introduce at the geometrical level a set of thirteen predicates constituting an extension of
250 Orientation in French Spacial Expressions
Allen's relations6 (R) (Allen 1 984). Each formula R(x, y, D) indicates the configuration between the maximum intervals filled by the individuals x and y in the direction D? Beside the classical axioms related to Allen's relations we introduce here a postulate stating that for every pair ofconnected individuals x and y and every direction D, one of the relations m, o, s, d, for - stands between them: A I 2 Vx, y, D C(x, y) � mosdf
=
�oisidi�(x, y, D)8
Defs Ex�y. x, d) =derLimi(y, x) 1\ Vv((P(v, x) 1\ --.P(v, y)) � <m(v, y, D)) It can be observed that, in some cases, for two given individuals x and y (for instance, when we are faced with the vertex y of a triangle x) several directions may verify this relation. Generally, this occurs when a tangent to the surface cannot be associated with some particular point. If we wanted a unique direction to be selected, we would have to introduce more constraints or conditions. That is exactly what we do by introducing a relation 'Exts', which indicate that y is an extremity of x in the direction D, and z an extremity (of a part u of x) in the opposite direction: Def6 Exts(y, z, x, D) =derEx�y. x, D) 1\ 3u(P(u, x) 1\ P(y, u) 1\ Ex�z, u, - D) 1\ Salien�z, x) 1\ (--.3v Poin�z, v) V --.3v Point(y, v))) In this definition the predicate 'Salient' accounts for the visual and cognitive processes that lead us to select a geometrically salient individual z in the individual x. A further specification of this phenomenon requires a precise study of the underlying processes. The remainder of the definition ensures that this individual z constitutes an extremity in the direction -D and that one of these extremities is not punctual. Going back to the case of the triangle, such an additional condition allows us (by raking into account the orthogonal direction at the base of the triangle) to select a unique direction among the first set of directions. 3.2 3.2.1
Functional /eve/
Intrinsic orientation
Using the different tools we have built up to now at the geometrical level, and raking into account the properties of the entities themselves, we can tackle the
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We state that y is an extremity of x in a direction D if y is a limit of x (as underlined above, the concept of limit has been already formalized at the geometric level of our representation system), and furthermore if every individual included in x (and not included in y) precedes or meets y in this direction D:
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formalization of the orientational process. In this paper, we consider first the intrinsic case, examining only vertical and frontal orientation, that is, leaving aside the lateral case; the deictic case, as well as all contextual cases, is eventually grounded on the intrinsic orientation of some entity. Consequently, the latter is studied in the definition section (section 3.2.2). Basing our analysis on the remark we made about the importance of the extremity notion for intrinsic orientation, we introduce a new partial function mapping an extremity y of an entity x (and an extremity z of a portion of x) on to the corresponding direction D: Def7
Vx, y, z, D dir-ext(y, z, x)
=
D
�
(Part(y, x) 1\ Part(z, x) 1\
Exts(stref(y), stref(z), stref(x), D)) and z ofx. The above axiom which directly handles entities and not simple portions of space9 relies on the geometric relation 'Exts' (indicating that the individual stref(y) constitutes an extremity of stref(x) in a direction) as well as on the part whole relations between entities already defined in our system. Starting with the vertical intrinsic orientation, a particular direction of an entity can be considered as its upper intrinsic direction if, in a canonical position, this direction coincides with the gravitational upper direction. We 1 express these conditions by means of the following definition: 0 Def8 Orient-haut(D, x) =der 3y, z(dir-ext(y, z, x) (In-Use(x) > dir-ext(y, z, x)
=
=
D
1\ Can-Use(x) 1\
haut-grav))
In this definition, the predicate 'Can-Use' ensures that the entity x has a canonical use. The predicate 'In-Use' together with the non-monotonic implication (> denoting an implicature) allows us to resrrict the coincidence of the directions to 'normal' (canonical) uses of x. We think that the non monotonic logic proposed in (Asher & Morreau 1 99 1 ) could be a good framework for handling such information.
A similar formula specifies a lower inrrinsic orientation, and a biconditional links it to the previous upper orientation: Defg Orient-bas(D, x) =def 3y, z (dir-ext(y, z, x) - D
A Can-Use(x) A
(In-Use(x) > dir-ext(y, z, x) - bas-grav))
AI 8
haut-grav � - (bas-grav)
The processing of frontal orientation calls for more complex mechanisms that mirror more complex phenomena. We thus distinguish three cases, which, as we shall see, are not mutually exclusive. The first case occurs when the frontal orientation of an entity x is induced by what Vandeloise calls the 'general orientation' of x (Vandeloise 1986a), which
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Henceforth we will say that such a direction is generated by the extremities y
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depends on various factors such as the direction of motion, the arrangement of the perception apparatus etc. So we first state that a given direction of an entity x may be considered as a front direction of type 1 if that direction x coincides with its general orientation: Def10 Orient-avann(D, x) =def3y, z dir-ext(y, z, x)
=
D 1\ Orient-gen(x, D)
Defi 1 Orient-avant2(D, x) =def3y, z{dir-ext(y, z, x) D 1\ Can-Use(x) 1\ Vu, D'{{Urilize(x, u) 1\ Orient-avann{D', u)) > D' - dir-ext(y, z, x))) =
This second case of frontal orientation which we call tandem orientation occurs with chairs, cars, clothes, etc. The third and last rule corresponds to entities whose frontal direction is opposed, in canonical use, to the user's frontal direction (cupboards, computers, TVs, etc.): Def12 Orient-avant3(D, x) =def3y, z(dir-ext(y, z, x) - D 1\ Can-Use(x) 1\ Vu, D'{{Urilize(x, u) 1\ Orient-avann(D', u)) > D ' - -dir-ext{y, z, x))) Finally, we express through the following rules that every entity having an intrinsic frontal orientation falls into one of these three cases and that front and back (intrinsic) directions stand in a relation of opposition: Def1 3 Orient-avant(D, x) =def Orient-avann(D, x) V Orient-avant2(D, x) V Orient-avant3{D, x) Vx, D Orient-avant(D, x) � Orient-arriere(-D, x) The formalization of the lateral cases, which is not completely worked out for rhe movement, is not considered in this paper. However, it can be underlined that this lateral modality calls for already more complex representa tions than frontal orientation does (which, as we just saw, is itself more complex than the vertical one). This property of our formal tools seems to match perfectly the observations made by psycholinguists about the acquisition and manipulation of orientation notions (Pierart 1 979). 3 .2.2
Definitions
Thanks to all the geometrical and functional tools introduced above, we can now express the 'crude' semantics of various internal and external localization
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We find in this category human beings, animals, arrows, but also cars and vehicles in general.U The second kind of frontal orientation covers all of the entities whose frontal direction coincides, in canonical use, with the frontal direction of the user. So, by means of this second rule, we state that a specific direction of an entity x constitutes a front direction of type 2 if the front direction ofevery entity using x in a canonical way coincides with this direction of x:
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lexemes. In particular, we will especially consider the formalization of their semantic component relative to orientation.
3.2.2.1 Intemal localization Let us start with Internal Localization Nouns (ILNs) and more precisely with the definition of the haut (top) of an entity. Intuitively, the intrinsic top corresponds to the portion of the entity situated in the pole whose direction is the intrinsic upper direction. Consequently, we state by means of the following definition that an entity y constitutes the intrinsic top of an entity x if y is the maximal element situated in the pole of x whose direction is D, and further more, if this direction corresponds to the intrinsic upper direction of x:
The direction D appearing in this predicate 'Haut-i' plays a very important part for the distinction between intrinsic and deictic top cases. In the case of an intrinsic top this direction comes from the entity itself, whereas in a deictic situation, it is given by another element of the context (the speaker) and does not have any special relation with the entiry: 12 Defi S Haut-d(y, x, D) =der 3s(Orient-haut(D, s) 1\ s � x 1\ Speaker(s) 1\ ln-pole(y, x, D) 1\ Vw(In-pole(w, x, D) � Part(w, y))) As we pointed out before, and in accordance with some experiments made by psychologists and psycholinguists (Carlon-Radvansky & Irwin 1 993), these vertical deictic uses are much more acceptable when they coincide with vertical contextual uses, that is to say, when the intrinsic upper direction of the speaker coincides with the gravitational up. In consequence, although in this study as a whole we do not consider contextual cases other than deictic ones, the contextual use of haut (top) seems an important configuration to describe:
Def16 Haut-c(y, x, haur-grav) =def ln-pole(y, x, haur-grav) 1\ V w(In-pole(w, x, haur-grav) � Part(w, y)) We give below the definitions corresponding to the concept of pole (and inclusion in a pole). Basically we can say that the pole y of an entity x in a direction D is constituted by the portion of x extending from the middle of x to its extremity in the direction D. These rules essentially rely on Allen's relations between the spatio-temporal referents of the previously mentioned entities (middle, extremity, etc.) in the direction D: Defi 7 Pole(y, x, D) =der 3e, m (Part(y, x) 1\ Middle(m, x) 1\ Ext(srref{e), stref{x), D) 1\ rn(stref{m), srref{y), D) 1\ f{stref{e), stref{y), D)) Defi 8 In-pole(y, x, D) =der 3u(Pole(u, x, D) 1\ Part(y, u))
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Def14 Haut-i(y, x, D) =der Orient-haut(D, x) 1\ In-pole(y, x, D) 1\ Vw (In-pole(w, x, D) � Part(w, y))
254 Orientation in French Spatial Expressions
3.2.2.2 External localization
One of the goals of this study was to propose orientation tools which could be used to formalize the semantic content of internal as well as external localization lexemes. Now we are going to show how our orientational formalism help to express the meaning of the external preposition devant (in front of). We can say that an entity y is situated (intrinsically) in front of an entity x if y is included in the space portion situated in front of x (that is to say, the space portion delimited by means of x and its intrinsic frontal direction). In order to grasp such a configuration, we introduce the predicate In-sp(y, x, D) which specifies that an entity y is included in the space delimited by the entity x and the direction D. From a more formal point ofview, this is expressed by stating that a relation I11j or > stands between the spatia-temporal referents of y and x in the direction D:o Def19 In-sp(y, x, D) =def l11j >(stre�y), stre�x), D) Then we can characterize the fact that an entity y is situated intrinsically in front of an entity x, indicating that y has to be contained in the space delimited by x and the direction D, which in turn constitutes the intrinsic frontal direction of x: Def2o Etre-devant-i(y, x, D) =der Orient-avant(D, x) A In-sp(y, x, D) Here again the deictic use of the preposition devant (in front of) differs from the intrinsic use in the underlying direction given by a speaker describing the scene situated in front of him: Def21 Etre-devant-d(y, x, D) =der3s (Orient-avan�-D, s) A s 'F x A s 'F y A Speaker(s) A In-sp(y, x, D) A Etre-devant-i(x, s, -D))
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On the basis of our orientational tools, we can introduce similar formal representations for the ILNs bas (bottom), avant (front), am'ere (back). It is also possible to specify the semantic content of iLNs such as dess us (top extremity), dessous (bottom extremity), devant (front extremity), derriere (back extremity) using the same formalization of orientational phenomena. The only difference between the semantic definition of these lexemes and the representations associated with the ILNs haut, bas, avant, arriere, etc. is based on the topological and geometric aspects. For instance, the dess us (top extremity) of an entity is the uppermost surface (roughly) perpendicular to the upper direction and in contact with the exterior of the entity. We obviously need topological and geometric concepts here which are much more complex than the sole notion of pole in a direction. In Aurnague ( 1 991), several definitions are introduced in order to characterize what is an external surface perpendicular to a direction D and furthermost in this direction.
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The fact that the speaker is facing the landmark to which he gives a frontal orientation means that we consider a mirror configuration (between the orienting speaker and the landmark). This is expressed by the minus sign associated with the underlying direction of the predicate 'Orient-avant'. In fact, mirror deictic configurations are very frequent in French as opposed to tandem orientations which are less often used. 3 .2.3
Inferences
As we said previously in the description of our methodological choices, we wish
J.2. J . r Intrinsic-intrinsic case
An
example of an utterance made up of two intrinsic devant (in �rant of) prepositions is:1• Le tabouret est devant leJa uteuil
(The stool is in front of the armchair) LeJa uteuil est devant Max
(The armchair is in front of Max) Using the formal tools introduced for the preposition devant, we can give the following representation of these two sentences in which t, f. and m respectively denote the stool, the armchair, and Max:
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to obtain a semantic representation ofutterances allowing us to draw inferences which have to be in accordance with the deductions made by human beings. We already showed in (Aumague & Vieu 1 993) that the inferences we can draw with the formal definition dans (in), sur (on), as well as with ILNs such as haul (top), devant (front extremity), dessous (bottom extremity), match our common sense inruitions. For instance from le vase est sur le dessus de /'armoire (the vase is on the top extremity of the cupboard) we can deduce that le vase est sur le haul de /'armoire (the vase is on the top of the cupboard). We will not give here the different steps of such a reasoning because it essentially relies on topological, and not on orientational, considerations (the reason is that the lexemes haul (top) and dessus (top extremity) have a similar semantic content from an orientational point of view and differ only in terms of topological aspects). However, we shall set out some of the inferences and calculations we can make using the semantic definitions previously proposed for the external preposition devant (in front of). Looking at two sentences in which this preposition appears, we examine the results obtained by applying transitivity to their formal representations. We split the verification into three cases according to the deictic or intrinsic narure of the relation involved in each of the two sentences we combine.
256 Orientation in French Spatial Expressions
Etre-devant-i{t, f, di) Etre-devant-i(f, m, d2) From the predicate 'In-sp' appearing in che definition of 'Etre-devant' we can deduce the following Allen's relations between the spatio-cemporal referents of c, f, and m: m; > (streqc), srreqf), di) Ill; > (streqf), scef(m), d2).
Etre-devanc-i(c, m, d2) Orienc-avanc(d2, m) 1\ In-sp(c, m, d2) Consequently, we succeed in calculating char le tabouret est devant Max (the stool is in front of Max) intrinsically, given the cwo previous sentences and the additional constraint ensuring the coincidence between the intrinsic frontal direction of the armchair and Max. The imponance of chis constraint is illustrated by Figures I and 2. In che first case, the cwo intrinsic directions coincide and le tabouret est devant Max can be uttered, whereas in the second configuration they are different so char che previous deduction cannot be drawn. Although, for pictorial facilities, we have represented aligned entities with identical or opposed intrinsic directions, ic may be noted that, in accordance with the definitions we proposed for devant (in front of), directional prepositions do not require alignment along the underlying direc-
Figure 1
Figure 2
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A very imponanc parameter in the sense char ic affects the overall deduction process concerns the identity of the directions d I and d2 underlying che cwo relations 'Etre-devant'. If we know char these directions coincide (which is formally expressed by di - d2) we can, on che basis of the axioms associated with Allen's relations (here we use che theorem V x, y, z, Ill; > (x, y, D) 1\ Ill; > (y, z, D) => >(x, z, D)), deduce chat >(stref(c), srreqm), d2), which, in accordance with the definition of 'In-sp', entails In-sp(c, m, d2). Associating chis face with the information about frontal intrinsic orientation of m: Orient-avanc(d2, m) contained in che definition ofEtre-devant-i{f, m, d2), we obtain:
Michel Aumague 2 5 7
tion.15 Moreover, the blocking of the inferences based on transitivity occurs every time the directions associated with the relations are different and not only when they are opposed (as illustrated in the figures).
3.2.3.2 Deictic-deictic case In an utterance such as the following, the landmarks involved in the two prepositions devant take their orientation from the speaker:16
The speaker can linguistically express the fact that this description completely depends on its spatial position with respect to the configuration by adding at the beginning of each sentence, an expression such as vu d'ici (seen from here). The following facts (based on the formal tools we described above), with t, p. and 1 denoting respectively the stool, the plant and the light, express the semantic content of the previous sentences: Etre-devant-d(t, p, d) Etre-devant-d(p, 1, d) The identity of the directions underlying each relation 'Etre-devant' comes directly from the hypothesis we made about the uniqueness of the speaker uttering such sentences and about the instantaneous character of such texts (the speaker doesn't change position). The same direction being associated with the two deictic relations 'Etre-devant', we can here again calculate that In-sp(t, 1, d) and finally conclude that Etre-devant-d(t, 1, d), which means that le tabouret est devant le lampadaire (the stool is in front of the light, deictically). We do not specify all the calculation steps because they are very similar to what has been shown in the previous example. Obviously, if the underlying directions had been different, it would not have been possible to draw such an inference. This may occur only when the spatial configuration is described from different positions or points of view in the two sentences (the same speaker occupying distinct positions at different moments or two speakers situated at distinct positions at the same moment which our work does not address). Figures 3 and 4 highlight the fact that transitive deductions work when a single speaker (Max) applies his orientation to the landmarks (the plant and the light): in this case (Figure 3) the sentence le tabouret est devant le lampadaire (the stool is in front of the light, deictically) can be inferred. On the contrary, the presence of two speakers (Max and Arthur in Figure 4) describing the spatial configuration from distinct positions means that
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Le tabouret est devant le plante (The stool is in front of the plant) LA plante est devant le lampadaire (The plant is in front of the light)
2 5 8 Oriemarion in French Spatial Expressions
Figure 3
the sentence le tabou ret est devant le lamp adaire is neither true from Max's nor from Arthur's point of view. Let us consider now what kind of calculation may occur if the previous spatial configuration was described by means of an utterance composed of a deictic devant combined with a deictic derri!re (rather than two deictic devant): Le tabouret est devant Ia plante
(The stool is in front of the plant) Le lampadaire est derriere Iaplante
(The light is behind the plant ) With t, p. and 1 denoting once again the stool, the plant, and the light, the following formulas express the semantic content of the previous sentences:
Etre-devant-d{t, p, d) Etre-derriere-d(l, p, -d) From the definitions of'Erre-devant' and 'Erre-derriere' and the relation 'In sp' we can state the following facts in terms of extended Allen's relations:
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Figure 4
Michel Aumague 259 II\ > (stref{t), stref{p), d) II\ > (stre£{1), stref{p), -d)
The second expression being equivalent to II\ > (stref{p), stre£{1), d), transitivity axioms associated with Allen's relations allow us to deduce that II\ > (stref{t), stre£{1), d) which means that: In-sp(t, 1, d) We also know, from the definition of deictic 'Etre-devant', that there is a speaker s different from t and 1 (the stool and the light) who has an intrinsic front orientation corresponding to the direction -d: In order to prove Etre-devant-d(t, 1, d) it remains to be stated that 1 is situated (intrinsically) in front of s or, in other words, that this speaker s faces the light to which she/he is applying her/his frontal orientation. From the expression Etre-devant-d(t, p, d) we can deduce that the speaker s, who utters these sentences, is facing p: Etre-devant-i(p, s, -d) The predicate 'ln-sp' appearing in the definition of 'Etre-devant-i' tells us that: mi > (stref{p), stef{s), -d) This relation combined with II\ > (stre£{1), stref(p), -d) (previously mentioned) entails by transitivity II\ > (stre£{1), stref{s), -d) which means that In-sp(l, s, -d). Consequently we have: Etre-devant-i(l, s, d) � Orient-avant(-d, s) 1\ In-sp(l, s, -d) Grouping together all the facts we have stated up to now we can, as in the previous example, infer the following formal expression, which indicates to us that le tabouret est devant le lampadaire (the stool is in front of the light, deictically): Etre-devant-d(t, 1, d) � Orient-avant(-d, s) 1\ s =1- t 1\ s =1- 1 1\ Speaker(s) 1\ ln-sp(t, 1, d) 1\ Etre-devant-i(l, s, -d)) These calculations show that it is possible to draw identical deductions from utterances describing a spatial configuration by means of different but semantically equivalent external relations.
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Orient-avant(-d, s) 1\ s =1- t 1\ s =1- l 1\ Speaker(s)
260 Orienta cion in French Spacial Expressions
3-2·3·3 Intrinsic-deictic case The last case we consider here combines an intrinsic use of the relation 'Erre devant' with a deictic one:
Le tabouret est devant
leJa uteuil
(The stool is in front of the armchair) LeJa uteuil est devant le lampadaire (The armchair is in front of the light) From the formal representation of these sentences (Etre-devant-i(t, f, d 1 )
1\
Etre-devant-d(f, 1, d2)), and with the same kind of calculation as previously
le tabouret est devant le lampadaire (the stool is in front
Once again, the whole deductive process is conditioned by the coincidence between the intrinsic frontal direction of the armchair d 1 and the deictic frontal direction d2 given to the light by a speaker s. Figures 5 and
6 illustrate
respectively what happens when these directions are identical and when they are notP Before finishing the presentation of the functional level, it may be mentioned that the notions of distance and relative size between the trajector and the landmark play a great part in the semantics of most spatial prepositions. Actually, the importance of these notions increases when we consider combinations of the same relation (as in the utterances above), because they constitute factors that can block the application of transitivity. However, although distance and relative size rely on geometrical tools, their part is heavily affected by contextual factors. Consequently, such phenomena have to be described and formalised at the pragmatic level.
Figure 5
Figure 6
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applied, we can deduce that
of the light, deictically: Etre-devant-d(t, I, d2)).
Michel Aumague 26 1
3·3
Pragmatic level
As we said
Def22 Prio-axiale-horizr (y, x, D) =der3D (D' e Ortho(D) 1\ D' e Ortho(haut grav) 1\ oo;(stre�y), srre�x), D ')) Def23 Prio-axiale-horiz2(y, x, D) =der 3D (D' e Ortho(D) 1\ D' e Ortho(haut grav) 1\ s;f;d;(stre�y), stre�x), D')) Def24 Prio-axiale-horiz3(y, x, D) =der3D (D ' e Ortho(D) 1\ D' e Ortho(haut grav) 1\ sfd(stre�y), srre�x), D')) Def25 Prio-axiale-horiz4(y, x, D) =der3D (D' e Ortho(D) 1\ D' e Ortho(haur grav) 1\ = (srre�y), stre�x), D'))
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at the beginning, we introduce at this level the underlying principles people use in order to filter out the relations inferred wrongly, or in order to deduce more information than the discourse actually contains. The pragmatic level modifies the semantics obtained at the functional level according to context and world knowledge. We have not yet identified and formalized all the pragmatic factors arising in orientation phenomena, but we shall illustrate their role through the description of the axial priority principle. As we showed at the functional level, the semantic representation of the preposition devant {in front of) constrains the positions of the trajector and the landmark with respect to the frontal axis. The definition stated that as soon as the trajector y is further on the frontal direction (associated to x) than the landmark x, y can be described as being devant (in front of) x whatever its lateral position with respect to x is (y can be on the left of/in front of/on the right of x). Nevertheless, because of the context of utterance (spatial configuration surrounding x and y, intentions of the speaker, etc.), we may want to say that y est e:xactement devant x (y is exactly in front of x) or y est davantage devant x que ne /'est z (y is more in front of x than z is), etc. The influence of the context can also be such that only the entities y situated exactly in front of x will be described as being devant x. By reducing the degree of freedom on the lateral axis, this pragmatic phenomenon amounts to focusing on the frontal direction; we call this 'axial priority'. In order to formalize the axial priority phenomenon, we introduce several definitions constraining the position of two entities y and x (repre senting the tajector and the landmark) with respect to a horizontal direction D ' which is orthogonal to the focused direction D. In fact, we consider four cases of axial priority. The first one takes into account the cases o and o; {overlapping of the extension intervals) whereas the fourth corresponds to = (equality con figurations). For their part, the second and the third definitions of axial priority bring together respectively the relations s; d; f; (inclusion of x in y along D) and the converse ones, s, d, f (inclusion of y in x along D): 18
262 Orientation in French Spatial Expressions
Classifying the possible configuration of the entities on the lateral axis in such a way, we introduce a way of differentiating between the various entities situated devant (in front of) a given entity x. However, a complete formalization of this phenomenon of axial priority would require a precise study of the contextual elements leading to these restrictions.
4 CONCLUSION
be in front),
etre au-dessous de
(to be above), etc. We have shown that these
formal definitions could be used in order to draw inferences matching the conclusions of natural (i.e. human) reasoning. This modular representation of orientation (and more generally of space in language) constitutes, from this point of view, a real cognitive approach. It confirms the fact that the semantic analysis of spatial expressions must be justified in terms of 'non linguistic structures formation' as proposed by Lang
(1990). Ifwe go back to the goals we set for this study in the beginning, we may point out that both have been fulfilled because our formal tool correctly grasps the differences between intrinsic and deictic orientation, and can be used further more to deal with internal localization as well as external localization. Our guess is that these properties of the formalism correctly account for some of the mechanisms underlying the cognitive processing of orientation. Besides the point previously mentioned (notion of relative distance between traj ector and landmark, pragmatic phenomena, etc.), we expect to pursue this work along two main axes. From a formal point of view, we would want to be able to define directions from individuals so as to not introduce new elements in our basic ontology. This aspect is part of a broader purpose we pursue in our group which consists in elaborating a geometry (for linguistic structures of space) based only on individuals (Asher, Aurnague, & Vieu forthcoming). We are also trying to relate the behaviour of state directions involved in localization processes with dynamic directions underlying the expression of movement
{Asher et al. 1 994; Asher & Sablayrolles 1 995; Laur 1 99 1 ; Sablayrolles 1993 ). This integration of spatial and temporal data constitutes a necessity if one wants to analyse utterances describing moving or changing configurations. Concerning the cognitive aspects, we plan to elaborate, with various psycholinguists and psychologists, experimentation in order to test some of the
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By focusing our research on a detailed semantic analysis, we have proposed a formalization of orientation which allows us to represent the semantic content of spatial expressions such as le haut (the top), /'arriere (the back), etre devant (to
Michel Aumague 263
hypotheses related to our formal tools or in order to highlight important properties or concepts of orientation in language (Aumague et a/. 1 993). Received: I s.o7.94 Revised version received: 01 .02.95
MICHEL AURNAGUE Equipe de Reclrerclre en Syntaxe et Semantique URA I OJJ-CNRS Maison de Ia Recherche Universite de Toulouse-Le Mira if 5, allies Antonio Machado 31 o 58 Toulouse Cedex France e-mail:aurnague® iritfr.
I
2
I would like to thank Nicholas Asher, Myriam Bras, Laure Vieu, and the rwo anonymous referees for their advice and comments which enabled me to improve the content as well as the form of this work. I am also very grateful to Andree and Mario Borillo for their continuing encouragement and helpful remarks. In fact strif is not really a function as we do not presuppose the existence ofa space given a priori. It is just a notational trick to isolate purely geometrical aspects of entities from their functional aspects. Formally it can be defined as an equi7 valence class berween entities, which means that several entities may derermine the same space-time portion. For more details see Aurnague & Vieu ( I 993). In this work, we looked at siruations in which a deictic orientation is given to an intrinsically oriented entity. However, we adopt a strategy which gives priority to an intrinsic interpretation wirh respect to a deictic one. So when the analysed text calls for a spatial relation involving an intrinsically oriemed trajector, we first interpret this relation in its intrinsic sense. If the inferences induced by this intrinsic interpretation are not compatible with other elements of rhe rext, then we rry to make a deictic interpretation of the previously mentioned spatial relation.
4 A preliminary srudy and formalization of
external relations were made some years ago in our group by N. Hathour (Hathout I 989) which is akin on various points to the new formal tool we propose. This notion is necessary in order to grasp the semantic conrent of prepositions such as devant Iderriere (in fronr of/behind, §J.J). 6 This axiomatic which is grounded on six basic relations and their converse, plus entity (in total thirteen murually exclu sive relations), has been proposed in Allen ( I 984) in order to draw calculi on tem poral inrervals. It makes it possible to grasp rhe following configurations between rwo intervals x and y: (x, y) m(x, y) m;(x, y) o(x, y) O;(X. y) s(x, y) s;(x, y) f(x, y) f;(x, y) d(x, y) d;(x, y) x-y
x precedes y y follows x x meets y y meets x x overlaps y y overlaps x x starts y y starts x x finishes y y finishes x x is included (during) in y y is included in x
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N O TES
264 Orientation in French Spatial Expressions
7
9
10
e denoting an event and y/e representing a slice of y whose rime marches the rime of e, a spatio-remporal version of 'orient haur' should be: Orient-hau�D. x) =d.r3y. z Dir-ex�y.z,x) 0 1\ Can-Use(x) 1\ Ve((Event(e) 1\ e c, streQx)) � (In-Use(x, e) > dir-ex�y. z, x)/e - haur-grav/e)) Bur not a mere buller which can only rake a contextual orientation. It can be deduced (from the definition of vertical intrinsic orientation) char when the speaker is in a canonical position, the direction applied to the spatial configura tion coincides with the gravitational upper direction. This specification of 'In-sp' is sufficient because we only consider parallelepi pedic, spherical, or cylindrical entities. If we wanted to rake into account more complex shapes (amphirheatres, arches, and more generally curved objects) we would have to state a much more complicated formula. We tested the latter for some particular entities and we showed that some interesting inferential properties obtained on the basis of this simple version of 'In-sp' were lost. Obviously these two sentences may also be interpreted in a deictic way. We assume here that when a lexeme pointing out a target with an intrinsic frontal orientation is identified in the analysed text the intrinsic interpretation of the preposition devant is chosen by defaulc. The relative preference for the alignmenc of the entities involved in an external or directional preposition greatly depends on contexrual factors. For chis reason chis variable (geomerrical) feature has not been integrated in the semantic definition of the preposition devant (in front of) and is controlled at the pragmatic level. In this case there is no more ambiguity because the two landmarks do nor have any inrrinsic frontal orientation so chat only a deicric interpretation of rhe preposition devant is possible. In Figure 6, rhe deictic orientation of rhe -
11 12
13
14
1s
16
17
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8
Several axioms are inrroduced in order to describe composition operations on these relations. The consrraint of spatial connectedness on the srudied entities ensures chat the extension along a given direction is an interval. Moreover, one may feel it is necessary to express these relations fully in terrns of projections of the individuals on to a straight line and of calculations on the resulting intervals (as is usual with Allen's relations). Previously we had in our system a predicate of projection alone with several axioms specifying irs behav iour. However, this predicate has nor been used here because it would have implied manipulating 'abstract' srraighr lines, points, and intervals not having the same srarus as the ones defined in Section 2. 1 . We think char such a specification requires a preliminary study of the cog nitive processes underlying these opera tions of projection. On the basis of chis posrulare and using the definition of inclusion (relation P of Clarke) as well as several theorems related ro Allen's relations, it can be proved for instance char: Vx, y, 0 P(x, y) � sf - s; f;(x,y, D) The function srref gives us the portion of space-rime filled by an entity; as a resul t of the instantaneity constraint previously mentioned, this portion corresponds here to a specific temporal slice temporally bounded by rhe event (or state) intro duced by the NL spatial expression analysed. We indicated earlier that, in rhe frame work of this work, we consider only 'instantaneous' utterances. However, the properties of inrrinsic orientation we define here concern the whole life of the entity (or at least a significant parr of it) and therefore they muse have a spatio temporal reading. We are presently working on a temporal rranslarion of such definitions in which directions should be considered as extended over rime (like the other spatio-temporal individuals). With
Michel Aurnague 265 light given by the speaker Max (facing it) could also be interpreted as a contextual orientation of the light by the armchair. Although it is true that these two orientations coincide in the configuration depicted by Figure 6, we should recall that, in the framework of this study, we only take into account intrinsic and deictic orientational processes.
I 8 The numbering of these definitions does not necessarily imply a greater acceptance for the spatial relation under considera tion. For instance, although two entities verifying the axial priority 2, 3, or 4 will be more 'in front of' than if they were in the configuration I, it is not always clear which of the configurations 2, 3, or 4 is the best.
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]umal oJSnnantics
1 2: 2b