, Volume 87, Issue 2-3, pp 145-169
Date: 16 Nov 2007

Type Logics and Pregroups

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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.

Special Issue Categorial Grammars and Pregroups Edited by Wojciech Buszkowski and Anne Preller