Type Logics and Pregroups

Studia Logica 87 (2-3):145-169 (2007)
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Abstract

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 whose universe is an arbitrary monoid.

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10.1007/s11225-007-9083-4

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References found in this work

The Mathematics of Sentence Structure.Joachim Lambek - 1958 - Journal of Symbolic Logic 65 (3):154-170.
Linear Logic.Jean-Yves Girard - 1987 - Theoretical Computer Science 50:1–102.
Quantales and (noncommutative) linear logic.David N. Yetter - 1990 - Journal of Symbolic Logic 55 (1):41-64.
Substructural Logics.Peter Joseph Schroeder-Heister & Kosta Došen - 1993 - Oxford, England: Oxford University Press on Demand.

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