Section: Scientific Foundations
Sentence structure and logic: the interaction between syntax and semantics
Participants : Renaud Marlet, Richard Moot, Christian Retoré, Sylvain Salvati [ correspondent ] .
The principle of compositionnality, enounciated by Frege and formalized by Montague, makes syntax be the main window through which the meaning of natural language can be studied. This is the reason why mathematical linguistics is not only interested in the kinds of languages formalisms may describe, but also to the structures those formalisms assign to valid sentences. In his work Montague uses the lambda calculus so as to build the semantics of fragments of English, and the connection with the lambda calculus that the Curry-Howard correspondence naturally establishes with many kinds of intuitionnistic logics has made categorial formalisms quite popular for developing Montague semantics. But Montague's work may also be adapted to other syntactic formalisms and it gives some rather elegant formalization of semantics [62] .
In Montague's approach the syntactic structure of a sentence is also the structure of its meaning and thus a from a grammar à la Montague, one can extract a grammar of a language and a grammar of meaning. This leads to the study of languages of structures denoting meanings. In particular, as in Montague tradition, when meanings are represented as logical formulae, themselves represented as lambda terms, this leads to a study of languages of lambda terms.
Montague's approach is only a first step toward modeling semantics and it has several shortcomings. For example, the particular kind of transformation it uses to map syntactic structures to meanings sometimes require to model syntax in a way that is counter-intuitive. The truth-conditional and intentional models of meaning, even though they can explain some phenomena of entailment, are not relevant from a cognitive point of view [42] . It is also the case that the strict compositional principle does not hold in general, as the famous Geach examples show.
The interests of the project at the interface between syntax and semantics are oriented in three directions. First, it seems that the minimalist approach of syntax advocated by Chomsky provides a description of language that is very close to it semantics. Thus we try to provide techniques for giving semantics to minimalist grammars. Second the various representations of discourse semantics are a way to extend Montague semantics and to make it more sensitive to the context. Finally, we try to understand the expressive power of Montague semantics so as to assess its possibilities.
