Table of Contents
The overall objective of the The project is organized along three research directions: ## Syntax-Semantics Interface
The
Here, an important idea of Montague comes into play, namely, the “homomorphism requirement”: semantics must appear as a homomorphic image of syntax. While this idea is almost a truism in the context of mathematical logic, it remains challenged in the context of natural languages. Nevertheless, Montague’s idea has been quite fruitful, especially in the field of categorial grammars, where van Benthem showed how syntax ans semantics could be connected using the Curry-Howard isomorphism. This correspondence is the keystone of the syntax-semantics interface of modern type-logical grammars. It also motivated the definition of our own Abstract Categorial Grammars (ACG) Technically, an ACG consists simply of a (linear) homomorphism between two higher-order signatures. Extensive studies have shown that this simple model allows several grammatical formalisms to be expressed, providing them with a syntax-semantics interface for free. We intend to carry on with the development of the ACG framework. At the foundational level, we will define and study possible type theoretic extensions of the formalism, in order to increase its expressive power and its flexibility. At the implementation level, we will continue the development of an ACG support system. To consider the syntax-semantics interface as the starting point of our investigations allows us not to be committed to some specific syntactic theory. The Montagovian syntax-semantics interface, however, cannot be considered to be universal. In particular, it does not seem to be that well adapted to dependency and model-theoretic grammars. Consequently, in order to be as generic as possible, we intend to explore alternative models of the syntax-semantics interface. In particular, we will explore relational models where several distinct semantic representations can correspond to a same syntactic structure. ## Discourse DynamicsIt is well known that the interpretation of a discourse is a dynamic process. Take a sentence occurring in a discourse. On the one hand, it must be interpreted according to its context. On the other hand, its interpretation affects this context, and must therefore result in an updating of the current context. For this reason, discourse interpretation is traditionally considered to belong to pragmatics. The cut between pragmatics and semantics, however, is not that clear. We intend to apply to some aspects of pragmatics (mainly, discourse dynamics) the same methodological tools Montague applied to semantics. The challenge here is to obtain a completely compositional theory of discourse interpretation, by respecting Montague’s homomorphism requirement. We think that this is possible by using techniques coming from programming language theory, in particular, continuation semantics and the related theories of functional control operators.
We have indeed successfully applied such techniques in order to model the way quantifiers in natural languages may dynamically extend their scope What characterize these different dynamic phenomena is that their interpretations need information to be retrieved from a current context. This raises the question of the modeling of the context itself. At a foundational level, we have to answer questions such as the following. What is the nature of the information to be stored in the context? What are the processes that allow implicit information to be inferred from the context? What are the primitives that allow a context to be updated? How does the structure of the discourse and the discourse relations affect the structure of the context? These questions also raise implementation issues. What are the appropriate datatypes? How can we keep the complexity of the inference algorithms sufficiently low? ## Common Basic Lexical and Grammatical Resources
Even if our research primarily focuses on semantics and pragmatics, we nevertheless need syntax. More precisely, we need syntactic trees to start with. We consequently need grammars, lexicons and parsing algorithms to produce such trees. During the last years, we have developped the notion of interaction grammar Further primary resources are needed in order to put at work a computational semantic analysis of utterances and discourses. As we want our approach to be as compositional as possible, we must develop lexicons annotated with semantic information. This opens the quite wide research area of lexical semantics. Finally, when dealing with logical representations of utterance interpretations, the need for inference facilities is ubiquitous. Inference is needed in the course of the interpretation process, but also to exploit the result of the interpretation. Indeed, an advantage of using formal logic for semantic representations is the possibility of using logical inference to derive new information. From a computational point of view, however, logical inference may be highly complex. Consequently, we need to investigate which logical fragments can be used efficiently for natural language oriented inference. ^{1)}
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h. de Groote. Towards a Montagovian account of dynamics. In M. Gibson and J. Howell (editors), Semantics and Linguistic Theory (SALT) 16, CLC Publications, pp. 1-16, 2006.^{3)}
B. Guillaume and G. Perrier. Interaction Grammars. Research on Language and Computation, 7:171-208, 2009.^{4)}
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