Wojciech Buszkowski Type Logics and Pregroups

Type Logics and Pregroups

We discuss the logic of pregroups, introduced by Lambek [34], and its connections with other type logics and formal grammars. The paper contains some new ideas and results: the cut-elimination theorem and a normalization theorem for an extended system of this logic, its P-TIME decidability, its interpretation in L1, and a general construction of (preordered) bilinear algebras and pregroups whos...

Lambek Grammars Based on Pregroups

Lambek [13] introduces pregroups as a new framework for syntactic structure. In this paper we prove some new theorems on pregroups and study grammars based on the calculus of free pregroups. We prove that these grammars are equivalent to context-free grammars. We also discuss the relation of pregroups to the Lambek calculus.

Lambek Calculus and Substructural Logics

Pregroup Grammars with Letter Promotions

We study pregroup grammars with letter promotions p ⇒ q. We show that the Letter Promotion Problem for pregroups is solvable in polynomial time, if the size of p is counted as |n| + 1. In Mater and Fix [9], the problem is shown NP-complete, but that proof assumes the binary (or decimal, etc.) representation of n in p, which seems less natural for applications. We reduce the problem to a graph-t...

Some Syntactic Interpretations in Different Systems of Full Lambek Calculus

[8] defines an interpretation of FL without 1 in its version without empty antecedents of sequents (employed in type grammars) and applies this interpretation to prove some general results on the complexity of substructural logics and the generative capacity of type grammars. Here this interpretation is extended for nonassociative logics (also with structural rules), logics with 1, logics with ...