The Review of Symbolic Logic

Research Article

BELIEF REVISION IN NON-CLASSICAL LOGICS

DOV GABBAYa1 c1, ODINALDO RODRIGUESa1 c2 and ALESSANDRA RUSSOa2 c3

a1 Department of Computer Science, King's College London

a2 Department of Computing, Imperial College

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 $L$, the approach enables the definition of belief revision operators for $L$, 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.

(Received December 18 2007)

Correspondence:

c1 DEPARTMENT OF COMPUTER SCIENCE, KING'S COLLEGE LONDON LONDON WC2R 2LS, UK E-mail: dov.gabbay@kcl.ac.uk

c2 DEPARTMENT OF COMPUTER SCIENCE, KING'S COLLEGE LONDON LONDON WC2R 2LS, UK E-mail: odinaldo.rodrigues@kcl.ac.uk

c3 DEPARTMENT OF COMPUTING, IMPERIAL COLLEGE, LONDON SW7 2BZ, UK E-mail: ar3@doc.ic.ac.uk