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Type Logics and Pregroups

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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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Authors and Affiliations

  1. Research Group on Mathematical Linguistics, Rovira i Virgili University in Tarragona, Tarragona, Spain

    Wojciech Buszkowski

  2. Faculty of Mathematics and Computer Science, Adam Mickiewicz University in Poznań, Poznan, Poland

    Wojciech Buszkowski

  3. Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, Olsztyn, Poland

    Wojciech Buszkowski

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  1. Wojciech Buszkowski
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Correspondence to Wojciech Buszkowski.

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

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Buszkowski, W. Type Logics and Pregroups. Stud Logica 87, 145–169 (2007). https://doi.org/10.1007/s11225-007-9083-4

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