Studia Logica

, Volume 87, Issue 2, pp 323–342

On the Logic of β-pregroups

Article

DOI: 10.1007/s11225-007-9090-5

Cite this article as:
Kiślak-Malinowska, A. Stud Logica (2007) 87: 323. doi:10.1007/s11225-007-9090-5
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Abstract

In this paper we concentrate mainly on the notion of β-pregroups, which are pregroups (first introduced by Lambek [18] in 1999) enriched with modality operators. β-pregroups were first proposed by Fadda [11] in 2001. The motivation to introduce them was to limit (locally) the associativity in the calculus considered. In this paper we present this new calculus in the form of a rewriting system, prove the very important feature of this system - that in a given derivation the non-expanding rules must always proceed non-contracting ones in order the derivation to be minimal (normalization theorem). We also propose a sequent system for this calculus and prove the cut elimination theorem for it. As an illustration we show how to use β-pregroups for linguistical applications.

Keywords

Pregroupβ-pregroupnormalization theoremcut elimination

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Logic and Computer ScienceUniversity of Warmia and MazuryOlsztynPoland