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STABLE CANONICAL RULES

Published online by Cambridge University Press:  09 March 2016

GURAM BEZHANISHVILI ,
NICK BEZHANISHVILI  and
ROSALIE IEMHOFF
GURAM BEZHANISHVILI
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCES NEW MEXICO STATE UNIVERSITY LAS CRUCES NM 88003, USAE-mail: guram@math.nmsu.edu
NICK BEZHANISHVILI
Affiliation:
INSTITUTE FOR LOGIC, LANGUAGE AND COMPUTATION UNIVERSITY OF AMSTERDAM P.O. BOX 94242, 1090 GE AMSTERDAM THE NETHERLANDSE-mail: N.Bezhanishvili@uva.nl
ROSALIE IEMHOFF
Affiliation:
DEPARTMENT OF PHILOSOPHY UTRECHT UNIVERSITY JANSKERKHOFF 13A, 3512 BL UTRECHT THE NETHERLANDSE-mail: r.iemhoff@uu.nl
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Abstract

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We introduce stable canonical rules and prove that each normal modal multi-conclusion consequence relation is axiomatizable by stable canonical rules. We apply these results to construct finite refutation patterns for modal formulas, and prove that each normal modal logic is axiomatizable by stable canonical rules. We also define stable multi-conclusion consequence relations and stable logics and prove that these systems have the finite model property. We conclude the paper with a number of examples of stable and nonstable systems, and show how to axiomatize them.

Keywords

03B45Modal logicmulti-conclusion consequence relationaxiomatizationfiltrationmodal algebravarietyuniversal class
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 1 , March 2016 , pp. 284 - 315
Copyright
Copyright © The Association for Symbolic Logic 2016 

References

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