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CANONICAL FORMULAS FOR wK4

Published online by Cambridge University Press:  19 September 2012

GURAM BEZHANISHVILI  and
NICK BEZHANISHVILI
GURAM BEZHANISHVILI*
Affiliation:
Department of Mathematical Sciences, New Mexico State University
NICK BEZHANISHVILI*
Affiliation:
Department of Computing, Imperial College London
*
*DEPARTMENT OF MATHEMATICAL SCIENCES NEW MEXICO STATE UNIVERSITY LAS CRUCES, NM 88003-8001 E-mail: [email protected]
†DEPARTMENT OF COMPUTING IMPERIAL COLLEGE LONDON SOUTH KENSINGTON CAMPUS LONDON, SW7 2AZ, UK E-mail: [email protected]
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Abstract

We generalize the theory of canonical formulas for K4, the logic of transitive frames, to wK4, the logic of weakly transitive frames. Our main result establishes that each logic over wK4 is axiomatizable by canonical formulas, thus generalizing Zakharyaschev’s theorem for logics over K4. The key new ingredients include the concepts of transitive and strongly cofinal subframes of weakly transitive spaces. This yields, along with the standard notions of subframe and cofinal subframe logics, the new notions of transitive subframe and strongly cofinal subframe logics over wK4. We obtain axiomatizations of all four kinds of subframe logics over wK4. We conclude by giving a number of examples of different kinds of subframe logics over wK4.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 5 , Issue 4 , December 2012 , pp. 731 - 762
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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