Modeling the Dynamic Effects of Discourse: Principles and Frameworks

International audienceWhen studying the meaning of natural language expressions, sentence level provides a natural entry point. Its relevance of course depends on the focus we want to put on the meaning: as related to thought, to communication, to truth, etc. In this paper, we concentrate on the model theoretic view on meaning, in particular via first order logic representation. More specifically, we present phenomena that illustrate the challenges raised by discourse to truth-conditional semantics and compositionality. We show that proposals to address theses challenges rely on the additional device of contexts and on the way sentences can access and modify these contexts. This capability is usually referred to as the context change potential of a sentence. Depending on the phenomenon, the contexts need to represent different kinds of information: propositions, discourse referents, and variations on these elements. We also show that taking into account the rhetorical structure of discourse leads to even richer structuring of the context. Parallel to the presentation of the phenomena, we concentrate on formalisms giving an account of the dynamics of discourse. We introduce the well established formalisms of Discourse Representation Theory (DRT) Dynamic Predicate Logic (DPL) , and the more recently developed approach based on continuation semantics. Finally, we introduce Segmented Discourse Representation Theory (SDRT) that combines the effects of dynamics and discourse structure.La phrase représente un niveau d'entrée naturel dans l'étude du sens des expressions de la langue naturelle. Sa pertinence dépend bien sûr de la perspective que l'on souhaite mettre en avant sur le sens : celle relative à la pensée, celle relative à la communication, celle relative à la valeur de vérité... Dans cet article, nous nous concentrons sur la perspective donnée au sens par la théorie des modèles, en particulier par la représentation avec la logique du premier ordre. Plus spécifiquement, nous présentons des phénomènes illustrant les difficultés posées par le discours à la sémantique vériconditionnelle et à la compositionalité. Nous montrons que les propositions pour répondre à ces difficultés reposent sur l'utilisation de contextes et de la manière dons les phrases peuvent accéder à ce contexte et le modifier. Ce mécanisme est généralement appelé potentiel de changement du contexte d'une phrase. Suivant le phénomène considéré, le contexte doit représenter différents types d'informations : des propositions, des référents de discours, et des variations de ces éléments. Nous montrons également que la prise en compte de la structure rhétorique du discours conduit à une représentation encore plus riche du contexte. Parallèlement à l'exposé de ces phénomènes, nous présentons différents formalismes qui en rendent compte. Nous présentons la théorie des représentations discursives (DRT), de la logique des prédicats dynamique (DPL), ainsi que l'approche fondée sur les continuations proposée plus récemment. Enfin nous présentons la théorie des représentations discursives segmentées (SDRT) qui combine les effets de la dynamique et de la structure discursive

Extraction and coordination in phase structure grammar and categorial grammar

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Logic Programming of the Displacement Calculus

Abstract. The displacement calculus of Morrill, Valentín and Fadda (2011)[12] forms a foundation for type logical categorial grammar in which discontinuity is accommodated alongside continuity in a logic which is free of structural rules and which enjoys Cut-elimination, the subformula property, decidability, and the finite reading property. The calculus deploys a new kind of sequent calculus which we call hypersequent calculus in which types and configurations have not only external context but also internal context, in the case that they are discontinuous. In this paper we consider the logic programming of backward chaining hypersequent proof search for the displacement calculus. We show how focusing eliminates all spurious ambiguity in the fragment without antecedent tensors and we illustrate coding of the essential features of displacement. In this way we lay a basis for parsing/theorem proving for this calculus, which is being used and extended in a system CatLog currently under development

A count invariant for Lambek calculus with additives and bracket modalities

The count invariance of van Benthem (1991) is that for a sequent to be a theorem of the Lambek calculus, for each atom, the number of positive occurrences equals the number of negative occurrences. (The same is true for multiplicative linear logic.) The count invariance provides for extensive pruning of the sequent proof search space. In this paper we generalize count invariance to categorial grammar (or linear logic) with additives and bracket modalities. We define by mutual recursion two counts, minimum count and maximum count, and we prove that if a multiplicative-additive sequent is a theorem, then for every atom, the minimum count is less than or equal to zero and the maximum count is greater than or equal to zero; in the case of a purely multiplicative sequent, minimum count and maximum count coincide in such a way as to together reconstitute the van Benthem count criterion. We then define in the same way a bracket count providing a count check for bracket modalities. This allows for efficient pruning of the sequent proof search space in parsing categorial grammar with additives and bracket modalities.Peer ReviewedPostprint (published version

A Categorial Type Logic ⋆

Abstract. In logical categorial grammar (Morrill 2011[23], Moot and Retoré 2012[11]) syntactic structures are categorial proofs and semantic structures are intuitionistic proofs, and the syntax-semantics interface comprises a homomorphism from syntactic proofs to semantic proofs. Thereby, logical categorial grammar embodies in a pure logical form the principles of compositionality, lexicalism, and parsing as deduction. Interest has focused on multimodal versions but the advent of the (dis)placement calculus of Morrill, Valentín and Fadda (2011[21]) suggests that the role of structural rules can be reduced, and this facilitates computational implementation. In this paper we specify a comprehensive formalism of (dis)placement logic for the parser/theorem prover CatLog integrating categorial logic connectives proposed to date and illustrate with a cover grammar of the Montague fragment.

Controlling Extraction in Abstract Categorial Grammars

International audienceThis paper proposes an approach to control extraction in the framework of Abstract Categorial Grammar (ACG). As examples, we consider embedded wh-extraction, multiple wh-extraction and tensed-clauses as scope islands. The approach relies on an extended type system for ACG that introduces dependent types and advocates for a treatment at a rather abstract (tectogrammatical) level. Then we discuss approaches that put control at the object (phenogrammatical) level, using appropriate calculi.Cet article propose une approche au contrôle de l'extraction dans le cadre des grammaires catégorielles abstraites (ACG). Comme exemples, nous considérons les extractions-wh enchâssées, les extractions-wh multiples et les propositions complétives comme îlots pour la portée des quantificateurs. L'approche repose sur un système de type étendu pour les ACG. Il introduit les types dépendants et plaide pour un traitement au niveau abstrait. Nous discutons ensuite des approches qui mettent le contrôle au niveau objet en utilisant des calculs appropriés