Speaker
Lutz Straßburger
INRIA Saclay  IledeFrance
Talks at this conference:
Thursday, 17:30, J222 
Lambek Calculus with Banged Atoms for Parasitic Gaps 
Authors: Mehrnoosh Sadrzadeh and Lutz Straßburger Lambek Calculus is a noncommutative substructural logic for formalising linguistic constructions [1]. However, its domain of applicability is limited to constructions with local dependencies [2]. We propose here a simple extension that allows us to formalise a range of relativised constructions with long distance dependencies, notably medial extractions and the challenging case of parasitic gaps [3]. In proof theoretic terms, our logic combines commutative and noncommutative behaviour, as well as linear and nonlinear resource management [4]. This is achieved with a single restricted modality. But unlike other extensions of Lambek Calculus with modalities [5], our logic remains decidable, and the complexity of proof search (i.e., sentence parsing) is the same as for the basic Lambek calculus. Furthermore, we provide not only a sequent calculus, and a cut elimination theorem, but also proof nets [6]. Keywords. {Substructural Logics, Permutation and Contraction, Exponentials, Proof Nets, Polarised Systems, Natural Language, Relativisation, Long Distance Dependencies } References. Bibliography
