AGM-Like Paraconsistent Belief Change

Logic Journal of the IGPL 25 (4):632-672 (2017)
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Abstract

Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations.

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Author Profiles

Marcelo E. Coniglio
University of Campinas
Rafael Testa
University of Campinas

References found in this work

Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
Subjunctives, dispositions and chances.Isaac Levi - 1977 - Synthese 34 (4):423 - 455.
Belief contraction without recovery.Sven Ove Hansson - 1991 - Studia Logica 50 (2):251 - 260.
Reversing the Levi identity.Sven Ove Hansson - 1993 - Journal of Philosophical Logic 22 (6):637 - 669.

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