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
Categories (categorize this paper)
DOI 10.1305/ndjfl/1134397663
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 65,579
Through your library

References found in this work BETA

Combinators and Structurally Free Logic.J. Dunn & R. Meyer - 1997 - Logic Journal of the IGPL 5 (4):505-537.
Kripke Models for Linear Logic.Gerard Allwein & J. Michael Dunn - 1993 - Journal of Symbolic Logic 58 (2):514-545.
Two Extensions of the Structurally Free Logic LC.K. Bimbó & J. Dunn - 1998 - Logic Journal of the IGPL 6 (3):403-424.
Four-Valued Logic.Katalin Bimbó & J. Michael Dunn - 2001 - Notre Dame Journal of Formal Logic 42 (3):171-192.

View all 8 references / Add more references

Citations of this work BETA

Dual Gaggle Semantics for Entailment.Katalin Bimbó - 2009 - Notre Dame Journal of Formal Logic 50 (1):23-41.
Action Frames for Weak Relevant Logics.Igor Sedlár - 2015 - In Pavel Arazim & Michal Dančák (eds.), The Logica Yearbook 2014. College Publications. pp. 267-279.
2007-2008 Winter Meeting of the Association for Symbolic Logic.Jeffrey Remmel - 2008 - Bulletin of Symbolic Logic 14 (3):402-411.

Add more citations

Similar books and articles


Added to PP index

Total views
39 ( #280,944 of 2,461,809 )

Recent downloads (6 months)
7 ( #101,349 of 2,461,809 )

How can I increase my downloads?


My notes