Proof nets for linguistic analysis

This book investigates the possible linguistic applications of proof nets, redundancy free representations of proofs, which were introduced by Girard for linear logic. We will adapt the notion of proof net to allow the formulation of a proof net calculus which is soundand complete for the multimodal Lambek calculus. Finally, we will investigate the computational and complexity theoretic consequences of this calculus and give an introduction to a practical grammar development tool based on proof nets

Parsing for Semidirectional Lambek Grammar is NP-Complete

We study the computational complexity of the parsing problem of a variant of Lambek Categorial Grammar that we call semidirectional. In semidirectional Lambek calculus SDL there is an additional non- directional abstraction rule allowing the formula abstracted over to appear anywhere in the premise sequent's left-hand side, thus permitting non-peripheral extraction. SDL grammars are able to generate each context-free language and more than that. We show that the parsing prob- lem for semidirectional Lambek Grammar is NP-complete by a reduction of the 3-Partition problem

Parsing for Semidirectional Lambek Grammar is NP-Complete

We study the computational complexity of the parsing problem of a variant of Lambek Categorial Grammar that we call semidirectional. In semidirectional Lambek calculus SDL there is an additional nondirectional abstraction rule allowing the formula abstracted over to appear anywhere in the premise sequent's left-hand side, thus permitting non-peripheral extraction. SDL grammars are able to generate each context-free language and more than that. We show that the parsing problem for semidirectional Lambek Grammar is NP-complete by a reduction of the 3Partition problem. Key words: computational complexity, Lambek Categorial Grammar 1 Introduction Categorial Grammar(CG) and in particular Lambek Categorial Grammar (LCG) have their well-known benefits for the formal treatment of natural language syntax and semantics. The most outstanding of these benefits is probably the fact that the specific way, how the complete grammar is encoded, namely in terms of `combinatory potentials' of its wor..