Section: Overall Objectives
Overall objectives
Computational linguistics is a discipline at the intersection of computer science and linguistics. On the theoretical side, it aims to provide computational models of the human language faculty. On the applied side, it is concerned with natural language processing and its practical applications.
From a structural point of view, linguistics is traditionally organized into the following subfields:

Syntax, the study of language structure, i.e., the way words combine into grammatical phrases and sentences.

Semantics, the study of meaning at the levels of words, phrases, and sentences.

Pragmatics, the study of the ways in which the meaning of an utterance is affected by its context.
Computational linguistics is concerned by all these fields. Consequently, various computational models, whose application domains range from phonology to pragmatics, have been developed. Among these, logicbased models play an important part, especially at the “higher” levels.
At the level of syntax, generative grammars [34] may be seen as basic inference systems, while categorial grammars [44] are based on substructural logics specified by Gentzen sequent calculi. Finally, modeltheoretic grammars [55] amount to sets of logical constraints to be satisfied.
At the level of semantics, the most common approaches derive from Montague grammars, [45] , [46] , [47] which are based on the simply typed $\lambda $calculus and Church's simple theory of types [35] . In addition, various logics (modal, hybrid, intensional, higher order...) are used to express logical semantic representations.
At the level of pragmatics, the situation is less clear. The word pragmatics has been introduced by Morris [50] to designate the branch of philosophy of language that studies, besides linguistic signs, their relation to their users and the possible contexts of use. The definition of pragmatics was not quite precise, and for a long time several authors have considered (and some authors are still considering) pragmatics as the wastebasket of syntax and semantics [30] . Nevertheless, as far as discourse processing is concerned (which includes pragmatic problems such as pronominal anaphora resolution), logicbased approaches have also been successful. In particular, Kamp's Discourse Representation Theory [42] gave rise to sophisticated `dynamic' logics [39] . The situation, however, is less satisfactory than it is at the semantic level. On the one hand, we are facing a kind of logical “tower of Babel”. The various pragmatic logicbased models that have been developed, while sharing underlying mathematical concepts, differ in several respects and are too often based on ad hoc features. As a consequence, they are difficult to compare and appear more as competitors than as collaborative theories that could be integrated. On the other hand, several phenomena related to discourse dynamics (e.g., context updating, presupposition projection and accommodation, contextual reference resolution...) are still lacking deep logical explanations. We strongly believe, however, that this situation can be improved by applying to pragmatics the same approach Montague applied to semantics, using the standard tools of mathematical logic.
Accordingly:
The overall objective of the Sémagramme project is to design and develop new unifying logicbased models, methods, and tools for the semantic analysis of natural language utterances and discourses. This includes the logical modelling of pragmatic phenomena related to discourse dynamics. Typically, these models and methods will be based on standard logical concepts (stemming from formal language theory, mathematical logic, and type theory), which should make them easy to integrate.
The project is organized along three research directions (i.e., Syntaxsemantics interface, Discourse dynamics, and Common basic resources), which interact as explained in the following paragraphs.
Syntaxsemantics interface
The Sémagramme project intends to focus on the semantics of natural languages (in a wider sense than usual, including some pragmatics). Nevertheless, the semantic construction process is syntactically guided, that is, the constructions of logical representations of meaning is based on the analysis of the syntactic structures. We do not want, however, to commit ourselves to such or such specific theory of syntax. Consequently, our approach should be based on an abstract generic model of the syntaxsemantic interface.
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 CurryHoward isomorphism [63] . This correspondence is the keystone of the syntaxsemantics interface of modern typelogical grammars [48] . It also motivated the definition of our own Abstract Categorial Grammars [58] .
Technically, an Abstract Categorial Grammar consists simply of a (linear) homomorphism between two higherorder signatures. Extensive studies have shown that this simple model allows several grammatical formalisms to be expressed, providing them with a syntaxsemantics interface for free. [59] , [61] , [62] , [53] , [43] , [54]
We intend to carry on with the development of the Abstract Categorial Grammar 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 Abstract Categorial Grammar support system.
As said above, to consider the syntaxsemantics interface as the starting point of our investigations allows us not to be committed to some specific syntactic theory. The Montagovian syntaxsemantics interface, however, cannot be considered to be universal. In particular, it does not seem to be that well adapted to dependency and modeltheoretic grammars. Consequently, in order to be as generic as possible, we intend to explore alternative models of the syntaxsemantics interface. In particular, we will explore relational models where several distinct semantic representations can correspond to a same syntactic structure.
Discourse dynamics
It 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.
As we mentioned above, 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 [57] , [31] , [32] , [56] and the related theories of functional control operators [36] , [37] .
We have indeed successfully applied such techniques in order to model the way quantifiers in natural languages may dynamically extend their scope [60] . We intend to tackle, in a similar way, other dynamic phenomena (typically, anaphora and referential expressions, presupposition, modal subordination...).
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 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 [40] as a model of natural language syntax. This includes the development of grammar for French, [52] together with morphosyntactic lexicons. We intend to continue this line of research and development. In particular, we want to increase the coverage of our French grammar, and provide our parser with more robust algorithms.
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.