Interaction Grammars

arXiv:0809.0494v1 [cs.LO] 2 Sep 2008 ISSN 0249-6399 ISRN INRIA/RR--6621--FR+ENG Thème SYM INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE Interaction Grammars Bruno Guillaume — Guy Perrier N° 6621 Septembre 2008 Centre de recherche INRIA Nancy – Grand Est LORIA, Technopôle de Nancy-Brabois, Campus scientifique, 615, rue du Jardin Botanique, BP 101, 54602 Villers-Lès-Nancy Téléphone : +33 3 83 59 30 00 — Télécopie : +33 3 83 27 83 19 Interaction Grammars Bruno Guillaume∗, Guy Perrier† Th`eme SYM — Syst`emes symboliques ´Equipe-Projet Calligramme Rapport de recherche n° 6621 — Septembre 2008 — 37 pages Abstract: Interaction Grammar (IG) is a grammatical formalism based on the notion of polarity. Polarities express the resource sensitivity of natural languages by modelling the distinction between saturated and unsaturated syntactic struc- tures. Syntactic composition is represented as a chemical reaction guided by the saturation of polarities. It is expressed in a model-theoretic framework where grammars are constraint systems using the notion of tree description and pars- ing appears as a process of building tree description models satisfying criteria of saturation and minimality. Key-words: Grammatical formalism, Categorial Grammar, Unification, Po- larity, Tree description ∗LORIA, INRIA Nancy Grand-Est (Bruno.Guillaume@loria.fr) † LORIA, Universit´e Nancy 2 (Guy.Perrier@loria.fr) Les Grammaires d’Interaction R´esum´e : Les grammaires d’interaction sont un formalisme grammatical bas´e sur la notion de polarit´e. Les polarit´es expriment la sensibilit´e aux ressources de la langue naturelle en distinguant les structures syntaxiques satur´ees et insa- tur´ees. La composition syntaxique peut ˆetre vue comme une r´eaction chimique control´ee par la saturation des polarit´es. Les grammaires sont exprim´ees par un syst`eme de contraintes utilisant la notion de description d’arbre. L’analyse syntaxique apparaˆıt alors comme un processus de construction de mod`eles sa- tisfaisant des crit`eres de neutralit´e et de minimalit´e. Mots-cl´es : Formalisme grammatical, Grammaires cat´egorielles, Polarit´e, Description d’arbre Interaction Grammars 3 Introduction Interaction Grammar (IG) is a grammatical formalism based on an old idea of O. Jespersen [20], L. Tesni`ere [46] and K. Adjukiewicz [2]: a sentence is viewed as a molecule with its words as the atoms; every word is equipped with a valence which expresses its capacity of interaction with other words, so that syntactic composition appears as a chemical reaction. The first grammatical formalism that exploited this idea was Categorial Grammar (CG) [39]. In CG, constituents are equipped with types, which ex- press their interaction ability in terms of syntactic categories. A way of high- lighting this originality is to use polarities: syntactic types can be represented by partially specified syntactic trees, which are decorated with polarities that express a property of non saturation; a positive node represents an available grammatical constituent whereas a negative node represents an expected gram- matical constituent; negative nodes tend to merge with positive nodes of the same type and this mechanism of neutralization between opposite polarities drives the composition of syntactic trees to produce saturated trees in which all polarities have been neutralized. The notion of polarity in this sense was not used explicitly in computational linguistics until recently. To our knowledge, A. Nasr was the first to propose a formalism using polarized structures [31]. Then, nearly at the same time, R. Muskens [30], D. Duchier and S. Thater [15], and G. Perrier [33] proposed grammatical formalisms using polarities. The latter was a first version of IG, presented in the framework of linear logic. This version, which covers only the syntax of natural languages, was extended to the semantics of natural lan- guages [35]. Then, S. Kahane showed that all well known formalisms (CFG, TAG, HPSG, LFG) can be viewed as polarized formalisms [21]. Unlike the pre- vious approaches, polarities are used in a non monotonous way in Minimalist Grammar (MG). E. Stabler [43] proposes a formalization of MG which highlights this. Polarities are associated with syntactic features to control movement inside syntactic structures: strong features are used to drive the movement of phonetic forms (overt movement) and weak features are used to drive the movement of logical forms (covert movement). With IG, we highlighted the fundamental mechanism of saturation between polarities underlying CG in a more refined way, because polarities are attached to the features used to describe constituents and not to the constituents them- selves — but the essential difference lies in the change of framework: CG are usually formalized in a generative deductive framework, the heart of which is the Lambek Calculus [23], whereas IG is formalized in a model-theoretic frame- work. A particular interaction grammar ap

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