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<?xml version="1.0" standalone="yes"?> <Paper uid="W02-0803"> <Title>Under-specification and contextual variability of abstract prepositions: a case study</Title> <Section position="4" start_page="0" end_page="0" type="metho"> <SectionTitle> 1 Introduction </SectionTitle> <Paragraph position="0"> Through the study of the preposition avec we discuss some major questions related to the analysis and model of abstract prepositions.</Paragraph> <Paragraph position="1"> Avec is traditionally (Spang-Hanssen, 1963) considered as a mixed preposition. On one side, its contextual behavior is very heterogeneous: contrary to the colored prepositions (e.g.</Paragraph> <Paragraph position="2"> spatial), it seems difficult to construct a unique sense from which all the meanings are derived; nevertheless, contrary to the uncolored prepositions such as de (of) or a (to) in French, avec seems to point to an identifiable set of constraints. It is our aim to investigate whether this set exists and to determine its status. This requires an answer to the following questions: 1. How can the contextual variability of polysemous prepositions be mastered ? 2. Does a privileged sense exists in the spectrum of this variability ? 3. What is the relation between sense and meanings ? 4. What criteria have to be filled by a model ? We discuss the first of these questions in section 2 where we present the theoretical contention around the notion of polysemy of grammatical items and prepositions in particular, against which we will have to evaluate the results of our study. The second question will be illustrated in section 3 where we present the main meanings of avec and focus on comitativity, which, being more abstract then the others, seems to point directly to the under-specified set of constraints defining avec in general. In section 4 we briefly introduce a model inspired from Channel Theory (Barwise and Seligman, 1997) and we test it on the problematic data related to the meaning of comitativity. In section 5 we come back to the two remaining questions: we present a model for the whole semantic domain of avec by introducing the distinction among notions and values and discuss the inferential power of our model.</Paragraph> <Paragraph position="3"> Following Pinkal's distinction between sense and meaning (Pinkal, 1985, Poesio, 1996), we consider that senses tell us under which circumstances in the world the sentence is true or false, and that meanings assigned to an expression behaves as functions from contexts to senses.</Paragraph> </Section> <Section position="5" start_page="0" end_page="0" type="metho"> <SectionTitle> 2 Polysemy and contextual variability </SectionTitle> <Paragraph position="0"> The notion of polysemy implies that (i) a word has many different meanings and that (ii) these meanings are in a certain way related to one another. A major issue is then to explain the phrase &quot;in a certain way&quot;. By virtue of what principles are they related? Is it by virtue of a July 2002, pp. 17-24. Association for Computational Linguistics. Disambiguation: Recent Successes and Future Directions, Philadelphia, Proceedings of the SIGLEX/SENSEVAL Workshop on Word Sense unique sense that, together with a rule system allows to generate all of them, or simply by virtue of family resemblances ? More fundamentally, the notion of polysemy poses the major question of the relation between language and thought. It is not only a matter of discovering whether a unique sense exists, but also to determine whether this sense is cognitively grounded, or in other terms, whether it is pre-linguistic or perception based.</Paragraph> <Paragraph position="1"> Cognitive linguists such as Wierzbicka (1996) claim that all meanings are derived from a cognitive primitive-based dictionary by a cognitive grammar. Under her account, language is grounded in thought and polysemy is a consequence of the instantiation of thought into language, the cognitive dictionary being the glue of all the meanings of a polysemous word.</Paragraph> <Paragraph position="2"> Wittgenstein (1953/1961) introduces in his Philosophical Investigations (SS68) a radically different point of view. He argues that it is clearly impossible to define words by abstract meanings on the account of pure observation.</Paragraph> <Paragraph position="3"> Provocative, this affirmation poses the problem of the existence of rules and opens a series of other questions: do definitions of polysemous word exist? And what do these definitions look like? Is it possible for an abstract definition to coexist with local values not caught by this definition? What is their status then? According to these antithetic philosophical positions, prepositions have undergone different treatments. Jackendoff (1987), Wierzbicka (1996) and Brondal (1950) consider that they instantiate primitive atomic notions and that their meanings can be metaphorically and metonymically calculated; some other authors such as Cadiot (1997) consider instead that prepositions denote different properties on a variable spectrum that cannot be reduced to an atomic sense.</Paragraph> <Paragraph position="4"> These positions are more often grounded in philosophical considerations rather than in empirical observations. Our approach is fundamentally inductive and is focused on the meaning of comitativity which seems to trace a privileged way to the abstract notion of avec.</Paragraph> </Section> <Section position="6" start_page="0" end_page="0" type="metho"> <SectionTitle> 3 The privileged status of comitativity </SectionTitle> <Paragraph position="0"> Let us first consider a classification of avec meanings.</Paragraph> <Paragraph position="1"> Thematic: Avec ce mauvais temps, il vaut mieux rester chez soi / By this bad weather, it is better to stay at home The meaning of comitativity, as argued by Cadiot (1997), stays in the middle of the spectrum of the semantic domain of the preposition avec: it is less constrained than the meaning of reciprocity and more specific than the meaning thematic. Compared to instrumental and manner, it is characterized by a notion of symmetry as will be discussed at length in the next section. Its privileged status clearly emerges from the definition given for the first time by Guillaume (1919/1975) and adopted by Cadiot (ibid.) in a recent study. Guillaume (ibid.: 279) defines the comitativity as follows1: &quot; the preposition avec is an abstract image of parallelism: it expresses the relation holding between two entities that exist or act together, accomplish the same movements and follow the same directions. This image presupposes a certain equality ... which is easily realized when the preposition links two nouns&quot;. Cadiot (ibid.: 153) adds to this the notion of interaction: &quot;avec creates ... the conditions for an optimal interaction between two entities of the reality&quot;.</Paragraph> <Paragraph position="2"> It is important to note that these definitions also apply to avec in general: according to these authors, they fit the meaning of comitativity and are modified into the other contextual possibilities enumerated in Table 1.</Paragraph> <Paragraph position="3"> 1 The translations are of the author of this paper. Three key notions emerge as fundamental from these citations: parallelism, interaction and finally association, which is strictly related to the first two. In the following section we show that the intuition grounding these definitions is correct, but that it is precisely the sense of association that needs an explanation: to define avec means to clearly formulate the constraints which need to be satisfied for two or more entities to be said &quot;associated&quot;. We admit that the meaning of comitativity has a privileged status and focus on it.</Paragraph> <Section position="1" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 3.1 Cadiot's account of comitativity </SectionTitle> <Paragraph position="0"> and problematic data On a phenomenological level, Cadiot (1997) analyzes the typical example of comitativity in (1), by a condition on symmetry (2) which implies a coordination (3): (1) Pierre marche avec Marie / Peter walks with Mary (2) a. If NP 1 VP avec NP2 then, NP2 VP avec NP1 b. If &quot;Pierre marche avec Marie&quot;, then &quot;Marie marche avec Pierre&quot; (3) a. If NP1 VP avec NP2, then NP1 VP et NP2 GV b. If &quot;Pierre marche avec Marie&quot;, then &quot;Pierre marche&quot; and &quot;Marie marche&quot; These conditions properly describe the fact that in a situation where &quot;Pierre walks with Mary&quot; it is true that &quot;Pierre walks&quot;, &quot;Marie walks&quot;, &quot;Pierre walks and Marie walks&quot;, &quot;Marie walks with Pierre&quot;.</Paragraph> <Paragraph position="1"> Nevertheless, these conditions appear too vague: all the cases enumerated from (4) to (6) below are unproperly generated by (2) and (3). Consider the case of two animates who are both at the same time in the same place2.</Paragraph> <Paragraph position="2"> (4) a. Jean s'est retrouve hier a la banque avec la voisine qu'il ne peut pas supporter / Tough he can't stand her, John was at the bank with his neighbor b. (??)Jean est a Paris avec Chirac / John is in Paris with Chirac The condition (2) which properly generates (4a) does not explain why (4b) is difficult to interpret if Jean lives in Paris and Chirac is in Paris as the President of the Republic and there 2 The symbol (??) means that the sentence is interpretable under specific conditions.</Paragraph> <Paragraph position="3"> is no interaction between them. The spatio-temporal association which seems sufficient for interpreting (4a) has to be reinforced by a stronger sense of interaction for (4b) to be interpretable.</Paragraph> <Paragraph position="4"> The condition in (2) also misses the difference between (5a) and (5b). Consider two inanimate entities: (5) a. Les verres sont dans le buffet avec les carafes / The glasses are in the cabinet with the pitchers b. (??)La porte est dans le salon avec la fenetre / The door is in the living-room with the window The sentence (5b) cannot describe the relation existing between a window and a door of a living-room. For it to be interpretable, the door and the window have to be figured out as taken down.</Paragraph> <Paragraph position="5"> Finally, the condition in (2) misses the constraints related to the nature of the predicates: (6) a. Jean est gentil avec Marie / John is kind with Mary b. (??)Jean est triste avec Marie / John is sad with Mary The only possibility to interpret (6b) is that Mary has an influence on John's sadness. The interpretation that John is sad, Mary is sad and that they are sad together at the same time, as foreseen by (2), is excluded.</Paragraph> <Paragraph position="6"> Of course these are all problematic data that a model of avec must explain. More abstractly, two major difficulties missed by (2) will have to be solved: (i) The spatio-temporal association problem. As discussed above (cf. (4a) / (4b)) the property of spatio-temporal location is not always sufficient to ensure the association of two entities.</Paragraph> <Paragraph position="7"> (ii) Regular association vs. accidental association. Consider two persons walking form point X to point Y. (7a) and (7b) describe this scene in a fundamentally different way: (7) a. Le passant A marche avec le passant B / Person A walks with person B b. Le passant A et le passant B marchent / Person A and person B walk (7a) means that the walk of the two persons is coordinated and that this coordination is not accidental. If one of the two persons turns around a corner, the other will do the same. This set of inferences is not enhanced by (7b), where et presents the coordination of the walks of the two persons as purely accidental.</Paragraph> <Paragraph position="8"> In the rest of the paper we will refer to (7a) as showing a togetherness effect. In the following section we introduce an intensional model which takes the mechanism of this effect into account.</Paragraph> </Section> </Section> <Section position="7" start_page="0" end_page="1" type="metho"> <SectionTitle> 4 Togetherness effect </SectionTitle> <Paragraph position="0"> The model we are about to present is an intentional model that takes into account the properties of the entities denoted by the NPs of the construction NP1 VP avec[+comitativity] NP2.</Paragraph> <Paragraph position="1"> This explanation contrasts with the extensional models that have been used to explain the togetherness effect (Lasersohn, 1998).</Paragraph> <Paragraph position="2"> Our representation serves the purpose of illustrating, by a concrete case, the speculative discussion in the next section. It can be questioned on many different formal aspects, and can be further elaborated or even differently expressed. Nevertheless the model is intuitive enough to ground the philosophical discussion underlying our case study.</Paragraph> <Section position="1" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 4.1 Shortcomings of extensional </SectionTitle> <Paragraph position="0"> models Lasershon (ibid.) proposes a model of togetherness based on the notion of group: (8) Together: given the eventuality3 e, a property P and a group g, together is appropriate iff g [?] P(e) and, for each part (proper or improper) e' of e, if it exists x such that x [?] P(e'), then P(e') = P(e).</Paragraph> <Paragraph position="1"> Under this account, a group is thought of in terms of the minimal number of entities sharing a property in an event (or state) and all its parts. As such, this model fails to discard the cases of pure accidental association such as (7b): this notion of group can be applied to a scene where two (and only two) persons accidentally walk in the street from point A to point B and in all the parts (proper and improper) of this path.</Paragraph> <Paragraph position="2"> 3 Eventualities are spatio-temporal entities such as states and processes (Binnick, 1991).</Paragraph> </Section> <Section position="2" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 4.2 Channel theory and intensionality </SectionTitle> <Paragraph position="0"> To explain the togetherness effect, we have developed a modal model inspired by Channel Theory of Barwise and Seligman (1997). We claim that the notion of togetherness is interpretable in terms of channel or the linkage of properties of the parts of a whole.</Paragraph> <Paragraph position="1"> A whole regulating and coordinating the internal behavior of its parts is a distributed system or channel. A model considering properties and types is intensional: knowing the object type, one can predict its behavior.</Paragraph> <Paragraph position="2"> A channel is thus defined by constraints that universally quantify over types (and not entities as in the extensional accounts), guaranteeing that the linkage of the properties of the parts (i) is regular (vs. accidental) for a given object type and (ii) take place within the structure of the distributed system.</Paragraph> <Paragraph position="3"> Technically, a channel is defined as the combination of two infomorphisms. The notion of classification grounds the definitions in (10) and (11).</Paragraph> <Paragraph position="4"> (9) Classification. A classification is a triple (Objets, Types, ), where Objets is a set of objects, Types a set of categories or types, and a relation between Objets and Types. If o [?] Objets and s [?] Types, o s means that the o is of type s.</Paragraph> <Paragraph position="5"> (10) Infomorphism. An infomorphism is a pair of such that, for o [?] Objects1 and s [?] Types2 : We claim that avec signals the presence of a distributed system regulating the properties of the entities it links, in a regular way. In other terms, the kind of association introduced by avec can be represented by a channel. We can thus formulate the abstract constraints defining the behavior of avec: (11) Under-specified sense of avec. Avec signals that the state of affairs it refers to is structured in a way that can be described by a channel.</Paragraph> </Section> <Section position="3" start_page="0" end_page="1" type="sub_section"> <SectionTitle> 4.3 Avec-comitativity </SectionTitle> <Paragraph position="0"> We can now come back to the explanation of the problematic data introduced in the discussion of avec-comitativity and test our model.</Paragraph> <Paragraph position="1"> The definition (12) establishes a clear distinction between (7a) and (7b): avec in (7a) signals the existence of an overall walk coordinating the two separate walks of the persons involved, where et in (7b) does not. It follows that only (7a) enhances a scenario that can be described by a channel. This under-specified definition is specified as follows into the meaning of comitativity: (12) Avec-comitativity. In a structure NP1 VP avec NP2, avec signals the existence of a channel verifying the following conditions: (i) it links the phases describing the events involving the entities denoted by NP1 and NP2, (ii) each of the phases involving one of the two entities implies that the phase involving the other entity expresses an actual or potential influence, (iii) no other phases than the ones described in the sentence can be evoked4.</Paragraph> <Paragraph position="2"> The following set of constraints further specify this representation (the operators F, P 4 This condition can be expressed by the notion of aggregation (Kratzer, 1989): the association has to be possible within the system itself and not by the intervention of external events.</Paragraph> <Paragraph position="3"> and have their usual meaning of past, future and possibility): For each , it exists such that Let us analyze this definition: (i) Avec links the eventualities which involve the entities denoted by NP1 and NP25. (ii) The types describing these eventualities are phases i.e. descriptions including the possible previous and past developments of the actual eventuality (Penczek, 1995).</Paragraph> <Paragraph position="4"> Moreover, we have to note that the constraints characterizing the channel present modal types. This is licit within Channel Theory and is particularly useful for our purposes. We can conclude that the channel signaled by avec-comitativity links the present, past and future developments of the eventualities which involve the denotations of NP1 and NP2.</Paragraph> <Paragraph position="5"> juxtaposition problem Let us come back to the paradox of spatio-temporal co-localisation. In most cases, avec is used when two entities interact. Cadiot (1997) considers this condition as necessary.</Paragraph> <Paragraph position="6"> Nevertheless some cases of pure spatio-temporal co-localisation are supported by avec, such as (4a). They can now be easily explained.</Paragraph> <Paragraph position="7"> Consider an example: (13) A son insu, Jean s'est retrouve sur la montagne avec un ours / Without knowing it, John was on the mountain with a bear In the referred state of affairs there is no interaction between John and the bear.</Paragraph> <Paragraph position="8"> Nevertheless, according to our experience, we know that the particular location of a person and a bear being on a mountain can evolve toward an interaction by virtue of them being in the same place. It is because John and the bear are in the same place at the same time, that they could interact. According to (13), this scenario can be described by a channel that takes the 5 From now on, we will refer to the denotations of NP and NP2 by X and Y respectively.</Paragraph> <Paragraph position="9"> form of potential interaction and links their mutual positions.</Paragraph> <Paragraph position="10"> This is not the case for the spatio-temporal location of John and Chirac in (4b). In the case where they would meet, it would not be by virtue of their being both in Paris, at least not in a default context; an extra eventuality should intervene for John et Chirac to meet and this is not allowed by (13) nor by the definition of channel in (11). There is then no distributed system regulating their particular spatio-temporal properties.</Paragraph> <Paragraph position="11"> The definition (13) also explains why in some other cases avec is impossible. Consider the window and the door of a living-room (5b): the properties of their spatio-temporal locations are not mutually regulated. This is why the interpretation of the sentence enhances a scenario in which someone has taken them down in the course of a remaking of the house, for instance.</Paragraph> <Paragraph position="12"> The same explanation holds for (6b). Avec forces an interpretation where the sadness (or another property) of Mary influences the sadness of John: avec signals a coordination of the properties of the entities it links. The definition in (12) forbids the interpretation that &quot;Jean is sad, Marie is sad, they are sad independently from one another and they are sad in the same spatio-temporal location&quot;.</Paragraph> <Paragraph position="13"> 5 A model for avec: notions, values, inferences Let us recall the argumentation we have been pursuing until now. Avec shows a very wide contextual variability and the challenge is to reconstruct a unique set of constraints explaining the coherence of its semantic spectrum. The meaning of comitativity has offered a privileged way toward this set defined in (12). This definition is quite abstract and is differently instantiated into the other contextual possibilities. The table 2 summarizes the definitions that can be given to each of the meanings listed in table 1.</Paragraph> <Paragraph position="14"> This table suggests that the meanings of avec can be classified into two families: the spatio-temporal trace and influence. The observable meanings, or values, differently instantiate the abstract constraints that we call notions.</Paragraph> </Section> </Section> <Section position="8" start_page="1" end_page="1" type="metho"> <SectionTitle> NOTIONS </SectionTitle> <Paragraph position="0"> aTwo entities are thought of as acting (or taking place) within the same scene in such a way that a connection exists between them.</Paragraph> <Paragraph position="1"> bWith connects phase by phase the two eventualities in which X and Y are involved without the intervention of eventualities other than the ones described in the sentence.</Paragraph> <Paragraph position="2"> gThe spatio-temporal trace of X gives an access to the spatio-temporal trace of Y without the intervention of entities other than the ones referred to in the sentence.</Paragraph> </Section> class="xml-element"></Paper>