Open Access
2005 Relational Semantics for Kleene Logic and Action Logic
Katalin Bimbó, J.~Michael Dunn
Notre Dame J. Formal Logic 46(4): 461-490 (2005). DOI: 10.1305/ndjfl/1134397663


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.


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Katalin Bimbó. J.~Michael Dunn. "Relational Semantics for Kleene Logic and Action Logic." Notre Dame J. Formal Logic 46 (4) 461 - 490, 2005.


Published: 2005
First available in Project Euclid: 12 December 2005

zbMATH: 1099.03014
MathSciNet: MR2183055
Digital Object Identifier: 10.1305/ndjfl/1134397663

Primary: 03B47
Secondary: 03B45 , 03D05 , 68Q70

Keywords: gaggle theory , join semi-lattice , Kleene star , Kripke semantics , modal logics , nonclassical logics , reflexive transitive closure , regular languages , residuation , Routley-Meyer semantics

Rights: Copyright © 2005 University of Notre Dame

Vol.46 • No. 4 • 2005
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