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<?xml version="1.0" standalone="yes"?> <Paper uid="C88-1077"> <Title>INTERPRETATION OF NOUN PHRASES IN INTENSIONAL CONTEXTS</Title> <Section position="3" start_page="0" end_page="0" type="intro"> <SectionTitle> 1. INTRODUCTION </SectionTitle> <Paragraph position="0"> Formally, an intension is a mapping that associates with eve,y possible world (actually, with indices that identify possible worlds) a denotation, where a denotation is a set of entities (individuals, relations, functions). If we take a term, say &quot;animal&quot;, it denotes, in the present world, a set of individuals; but the meaning of the term cannot be characterized by that set. For instance, the terms &quot;human&quot; and the term &quot;featherless biped&quot; denote the same set, but their meaning is different, since the fact that there are ~ featherless bipeds except human beings, in this world, e.'m be regarded as a mere accident. It is not difficult to conceive of a different world where another species shares the same property with humans.</Paragraph> <Paragraph position="1"> The characterization of possible worlds has been subject to deep philosophical debates, which were mainly concerned with the relationships existing between &quot;conceivable worlds&quot; and &quot;possible worlds&quot;, as well as with the connections existing between alternative worlds, but, for tim present purpose, we only need to note that: - The concept of &quot;possible world&quot; is rather easy to render formally, expanding the usual concept of interpretation in logics by introducing &quot;indices&quot; on worlds. Thus, for instance, the mapping which assigns to each predicate symbol a relation (of the same arity) on the universe, must be viewed as a set of mappings (one for each world), since the denotation of the predicate can vat 3, fiom world to world. Equivalently, the intension of a n-ary predicate can be delined as a function from world indices to n-sty relations.</Paragraph> <Paragraph position="2"> - The concept of &quot;possible world&quot; is rather common in the everyday practice. For instance, in saying (1) John seeks a unicorn no relation between John and a real world entity referred to by % unicorn&quot; can be assumed, since no such entity exists. Nonetheless (2) John seeks a centaur is different fi'om (1). Intuitively, the expression &quot;centaur&quot; has a meaning different fiom &quot;unicorn&quot;, because in some (fictitious) world they are used to refer to different entities. The same cannot be said for expressions such '.,s &quot;centaur&quot; and % being hall' human and half horse&quot;, since the second can be used to define the first ~.</Paragraph> <Paragraph position="3"> On the other hand, the fact that possible worlds are common to logics and intuition does not mean that there is an exact match in the way the concept is used.</Paragraph> <Paragraph position="4"> Let's consider, for instance, the best known treatment of natural language in logics, i.e, the work of Monlague's. In order to maintain the strict compositionality of his approach, Montaguc llad to make the interpretation of linguistic entities considerably complex a.</Paragraph> <Paragraph position="5"> For instance, the interpretation of a NP is given as a set of properties, where a property is a function from indices to set of individuals. For instance the property &quot;redness&quot; is that function that, for each index, says what is ted at that index. Of course, this is intuitively acceptable, but why should &quot;John&quot; be interpreted as a set of properties? It is true that with any person we know we associate a bundle of proper..</Paragraph> <Paragraph position="6"> ties that that person has (i.e properties such that the individual denoted by &quot;John&quot; happens to be in their denotation evaluated at this index), but it seems also true that when I say &quot;John&quot; I refer to an individual and not to his properties ~. Even more complex is tim treatment of NP's in object position; for instance the phrase &quot;a unicorn&quot; in (1) is interpreted as a property of properties, in order to accont for the fact that, loosely speaking, sets have to be evaluated &quot;here and now&quot; and so the set of properties that t, unicorn has is the same as the set of properties that a celltaur has.</Paragraph> <Paragraph position="7"> We cannot go in further details here (more detailed information can be found in \[Dowry et al. 81l), but a couple of questions naturally arises: Is it possible to maintain the basic principles of a possible worlds analysis without introducing the complexities of Montague's inmnsional logic? Is it possible to introduce an internlediate level in the semantic interpretation process, which preserves the idea of compositionality? Recently, two interesting proposals concerning the semantics of NL have been put forward. It seems that they can give some suggestions about how to answer the questions above. We will briefly outline them here, but we must first notice that we do not aim at presenting the philosophical position of those authors, since the discussion that follows is strongly biased to the views we hold about the 1 This can simply be due to my scarce knowledge about mythology. If there is a more precise characterization of centaurs, such that it is possible to conceive of a world where a being half human and half horse is not in the denotation of &quot;centaur&quot;, then the same situation as &quot;featherless biped&quot; arises.</Paragraph> <Paragraph position="8"> 2 We cannot discuss here our disagreement with a conception of syntax that assigns to a sentence as (1) two different syntactic stnmtures in order to cope with the so-called spec~c and non-specific readings (the one where a particular unicorn is wanted vs. the one where any unicorn could serve John's purpose). We can only note that, in our view, syntax is mainly concerned with surface phenomena. Note also that in \[Cooper 83\] a Montague-based proposal is presented, that overcomes this difficulty.</Paragraph> <Paragraph position="9"> 3 Formally, the two alternatives are equivalent if we assurae that no two individuals share the same &quot;total&quot; set of properties. For this reason, the solution proposed by Montague is perfect, if we assume, as he did, that no intermediate representation of the meaning of linguistic entities is ever built. In fact, the formulae of intensional loeics are only tools to renresent constraints on oossible worMs, so tha~ their complexities was not a matter at hand. As we will see, our position is different.</Paragraph> <Paragraph position="11"> The first proposal is &quot;Situation semantics&quot; by Barwise and Perry 1183\]. They view the meaning of a sentence as a relation between the discourse situation (who are the speaker, the addressee, etc.), the connections of the speaker (i.e. its relationships with the environmenl), and a described situation (the event, or &quot;type of event&quot;, which is being described). What is flmdamental, in our view, is the rejection o1' truth values as &quot;senses&quot; of sentences. This move accounts for the non-.equivalence of attitude reperts involving logically eqtdvalent embedded sentences. For instance, (3) John knows that two plus two is fonr is not the same as (4) .iohn knows that the square of 37 is 1369 although bt,th facts are necessary lruths (with respects to the difference Imtween meaning and intension, see also \[Lewis 72\]). Also important is the exploitatioo of what is called ,'esource situation in the interpretation of constituent of sentences. In the present concern~ we. can fix our attention on NP's. Let ItS consider, for example, the meaning of defufite noun phrases: &quot;We can also think of. d,c \[the n\] 4 as giving a partial function fi'um situations e to individuals a~,: d,c \[tbe u\] re) is defined and = ae iff d,c \[tile u\] a,,e &quot; IBarwise & Perry 8L pp.149-150\] where the latter means that in the context where tile expression is evaluated tb~ &quot;rehttionar' meaning of u umst single out exactly one individual. If we have available a particular resource situation, then we get an individual (a,,), but if such at context is not awdlable, then the interpretation of the NP is just the non-evaluated function fi'om situations to individuals. In the lirst case, we get the referential (or value-loaded) use, since any predicate the sentence expresses is about the referred individual (a~,); in the second case we get the attributive (or value-free) use; what is the predicate about in this case? It will be about the eventual (possible, future, fictional) fillet&quot; of rite description. The simplesl way to obtain such a resuh is to incorporate the description of the individual into tile inlerpretalion of the sentence, so that, whenever th.~ actual fillet&quot; will be avaihtble, the predicate will be true of it. This approach does not seem to us in contrast with a possible worlds analysis: in each such a world there will be all individual denoted by the definite CXl)ression (possibly different individuals at different indices); thus, the property of satisfying rite description will imply the property expressed by the predicate. In any case, the iuterpretatior, of sentences on the basis of some specific contextual situation suggests that the context is made explicit, in particular the connections of the speaker; of course, in an &quot;nnderstanding&quot; system (be it a human or a computer) such counectious are, at best, presumed, that is the hearer must &quot;imagine&quot; the connections on tire basis of a &quot;shared&quot; environment or whatever she/he knows about tile speaker. More important, in case the hearer is a machine, no real sharing of environment can be assumed, so that it must use an &quot;internal&quot; representation of the outer context; In the present work, this representation is available in terms of general world knowledge (represented in a KL..ONE like format), plus the history of the usermachine dialogue carried on so far.</Paragraph> <Paragraph position="12"> Another piece of research that must be taken into flccoant concorns mental apaces \[Fauconnier 8511. This framework provides us with a tool for representing the relationships between the individuals mentioned in a sentence and their particular view of reality. We believe that this is one of tire most common nses of the protheoretical notion of possible world. Of course, tile knowledge, the beliefs, the opinions, the desires of different persons are not the same, and when we want to understand natural language we must try to model these differences. Although mental spaces are not claimed to be such a modelling technique s, nonetheless they seem useful in modelling the process that leads to the construction of rite correct interpretation 6.</Paragraph> <Paragraph position="13"> 4 &quot;d&quot; stmtds for the discourse situation, c for the &quot;connections&quot;, &quot; \[the 1C/\] &quot; for file meaning of 'the 'g', &quot;e&quot; for the described situation.</Paragraph> <Paragraph position="14"> This paper does not present an implementation of the mental spaces approach, but uses one of the basic ideas of that work: some linguistic contexts &quot;set up&quot; local spaces that constrain the meaning of the entities occurring in them. So, a mental space represents a local view of linguistic entities, that may be used to isolate the (referred) beliefs, desires, etc., of the mentioned individuals.</Paragraph> <Paragraph position="15"> It should be clear from the above discussion that we are not adopting in full any of the positions of the reviewed works. It seems, however, that each of them can have a strong impact on the overall framework. Thus, an adaptation of mental spaces can help in modelling the process of building the meaning of sentences; a &quot;situational&quot; analysis can help in unde,'standing how such a meaning must merge wifll the environment; a possible world approach can provide the basic insights about the tinal result of the interpretation. This paper is mainly concerned whh the first of these three aspects.</Paragraph> </Section> class="xml-element"></Paper>