## Notre Dame Journal of Formal Logic

### Relational Semantics for Kleene Logic and Action Logic

#### Abstract

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.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 46, Number 4 (2005), 461-490.

Dates
First available in Project Euclid: 12 December 2005

https://projecteuclid.org/euclid.ndjfl/1134397663

Digital Object Identifier
doi:10.1305/ndjfl/1134397663

Mathematical Reviews number (MathSciNet)
MR2183055

Zentralblatt MATH identifier
1099.03014

#### Citation

Bimbó, Katalin; Dunn, J.~Michael. Relational Semantics for Kleene Logic and Action Logic. Notre Dame J. Formal Logic 46 (2005), no. 4, 461--490. doi:10.1305/ndjfl/1134397663. https://projecteuclid.org/euclid.ndjfl/1134397663

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