Notre Dame Journal of Formal Logic 46 (4):461-490 (2005)

Katalin Bimbo
University of Alberta
Kleene algebras and action logic were proposed to be solutions to the finite axiomatization problem of the algebra of regular sets (of strings). They are treated here as nonclassical logics—with Hilbert-style axiomatizations and semantics. We also provide intuitive accounts in terms of information states of the semantics which provide further insights into the formalisms. The three types of "Kripke-style'' semantics which we define develop insights from gaggle theory, and from our four-valued and generalized Kripke semantics for the minimal substructural logic. Soundness and completeness are proven each time
Keywords gaggle theory   Routley-Meyer semantics   Kripke semantics   nonclassical logics   modal logics   join semi-lattice   residuation   reflexive transitive closure   Kleene star   regular languages
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DOI 10.1305/ndjfl/1134397663
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2007-2008 Winter Meeting of the Association for Symbolic Logic.Jeffrey Remmel - 2008 - Bulletin of Symbolic Logic 14 (3):402-411.
Action Frames for Weak Relevant Logics.Igor Sedlár - 2015 - In Pavel Arazim & Michal Dančák (eds.), The Logica Yearbook 2014. College Publications. pp. 267-279.

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