TY - JOUR
T1 - Belief revision in non-classical logics
AU - Gabbay, Dov
AU - Rodrigues, Odinaldo
AU - Russo, Alessandra
N1 - Publisher Copyright:
© 2008 Association for Symbolic Logic.
PY - 2008/10/1
Y1 - 2008/10/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84989184384&partnerID=8YFLogxK
U2 - 10.1017/S1755020308080246
DO - 10.1017/S1755020308080246
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AN - SCOPUS:84989184384
SN - 1755-0203
VL - 1
SP - 267
EP - 304
JO - Review of Symbolic Logic
JF - Review of Symbolic Logic
IS - 3
ER -