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BELIEF REVISION IN NON-CLASSICAL LOGICS

Published online by Cambridge University Press:  01 October 2008

DOV GABBAY ,
ODINALDO RODRIGUES  and
ALESSANDRA RUSSO
DOV GABBAY*
Affiliation:
Department of Computer Science, King's College London
ODINALDO RODRIGUES*
Affiliation:
Department of Computer Science, King's College London
ALESSANDRA RUSSO*
Affiliation:
Department of Computing, Imperial College
*
*DEPARTMENT OF COMPUTER SCIENCE, KING'S COLLEGE LONDON LONDON WC2R 2LS, UK E-mail:[email protected]
†DEPARTMENT OF COMPUTER SCIENCE, KING'S COLLEGE LONDON LONDON WC2R 2LS, UK E-mail:[email protected]
‡DEPARTMENT OF COMPUTING, IMPERIAL COLLEGE, LONDON SW7 2BZ, UK E-mail:[email protected]
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Abstract

In this article, we propose a belief revision approach for families of (non-classical) logics whose semantics are first-order axiomatisable. Given any such (non-classical) logic , the approach enables the definition of belief revision operators for , in terms of a belief revision operation satisfying the postulates for revision theory proposed by Alchourrón, Gärdenfors and Makinson (AGM revision, Alchourrón et al. (1985)). The approach is illustrated by considering the modal logic K, Belnap's four-valued logic, and Łukasiewicz's many-valued logic. In addition, we present a general methodology to translate algebraic logics into classical logic. For the examples provided, we analyse in what circumstances the properties of the AGM revision are preserved and discuss the advantages of the approach from both theoretical and practical viewpoints.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 1 , Issue 3 , October 2008 , pp. 267 - 304
Copyright
Copyright © Association for Symbolic Logic 2008

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References

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