Type Logics and Pregroups |
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| Authors: | Wojciech Buszkowski |
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| Affiliation: | (1) Research Group on Mathematical Linguistics, Rovira i Virgili University in Tarragona, Tarragona, Spain;(2) Faculty of Mathematics and Computer Science, Adam Mickiewicz University in Poznań, Poznan, Poland;(3) Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, Olsztyn, Poland |
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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. Special Issue Categorial Grammars and Pregroups Edited by Wojciech Buszkowski and Anne Preller |
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| Keywords: | bilinear algebra pregroup Lambek calculus substructural logics |
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