On the Membership Problem for Non-Linear Abstract Categorial Grammars

International audienceIn this paper we show that the membership problem for second order non- linear Abstract Categorial Grammars is decidable. A consequence of that result is that Montague-like semantics yield to a decidable text generation problem. Furthermore the proof we propose is based on a new tool, Higher Order Intersection Signatures, which grasps statically dynamic properties of λ-terms and presents an interest in its own

Automatic F-Structure Annotation from the AP Treebank

We present a method for automatically annotating treebank resources with functional structures. The method defines systematic patterns of correspondence between partial PS configurations and functional structures. These are applied to PS rules extracted from treebanks. The set of techniques which we have developed constitute a methodology for corpus-guided grammar development. Despite the widespread belief that treebank representations are not very useful in grammar development, we show that systematic patterns of c-structure to f-structure correspondence can be simply and successfully stated over such rules. The method is partial in that it requires manual correction of the annotated grammar rules

A Generalised Quantifier Theory of Natural Language in Categorical Compositional Distributional Semantics with Bialgebras

Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier theory of natural language, due to Barwise and Cooper. The underlying setting is a compact closed category with bialgebras. We start from a generative grammar formalisation and develop an abstract categorical compositional semantics for it, then instantiate the abstract setting to sets and relations and to finite dimensional vector spaces and linear maps. We prove the equivalence of the relational instantiation to the truth theoretic semantics of generalised quantifiers. The vector space instantiation formalises the statistical usages of words and enables us to, for the first time, reason about quantified phrases and sentences compositionally in distributional semantics

On the Complexity of Free Word Orders

International audienceWe propose some extensions of mildly context-sensitive for- malisms whose aim is to model free word orders in natural languages. We give a detailed analysis of the complexity of the formalisms we propose

Type-theoretic extensions of Abstract Categorial Grammars

Abstract Categorial Grammars (ACG), in their original definition, are based on the linear λ-calculus. This choice derives from the traditional categorial grammars, which are based on resource sensitive logics. From a language-theoretic standpoint, this linearity constraint does not result in a weak expressive power of the formalism. For instance, the string languages generated by the second-order ACGs (whose parsing is known to be polynomial) corresponds to the class of mildly context sensitive lan- guages. From a more practical point of view, however, it would be interesting to increase the intentional expressive power of the formalism by providing high level constructs. For instance, one would like to provide the ACGs with feature structures, as it is the case in most current grammatical formalisms. In previous paper, a possible way of extending the ACGs is suggested. It consists of enriching the type system of the formalism with new type constructors. The present paper elaborates on this proposal

Lexicalized non-local MCTAG with dominance links is NP-complete

An NP-hardness proof for non-local Multicomponent Tree Adjoining Grammar (MCTAG) by Rambow and Satta (1st International Workshop on Tree Adjoining Grammers 1992), based on Dahlhaus and Warmuth (in J Comput Syst Sci 33:456–472, 1986), is extended to some linguistically relevant restrictions of that formalism. It is found that there are NP-hard grammars among non-local MCTAGs even if any or all of the following restrictions are imposed: (i) lexicalization: every tree in the grammar contains a terminal; (ii) dominance links: every tree set contains at most two trees, and in every such tree set, there is a link between the foot node of one tree and the root node of the other tree, indicating that the former node must dominate the latter in the derived tree. This is the version of MCTAG proposed in Becker et al. (Proceedings of the 5th conference of the European chapter of the Association for Computational Linguistics 1991) to account for German long-distance scrambling. This result restricts the field of possible candidates for an extension of Tree Adjoining Grammar that would be both mildly context-sensitive and linguistically adequate