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AGM-Like Paraconsistent Belief Change
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
Decrement Operators in Belief Change
While research on iterated revision is predominant in the field of iterated
belief change, the class of iterated contraction operators received more
attention in recent years. In this article, we examine a non-prioritized
generalisation of iterated contraction. In particular, the class of weak
decrement operators is introduced, which are operators that by multiple steps
achieve the same as a contraction. Inspired by Darwiche and Pearl's work on
iterated revision the subclass of decrement operators is defined. For both,
decrement and weak decrement operators, postulates are presented and for each
of them a representation theorem in the framework of total preorders is given.
Furthermore, we present two sub-types of decrement operators
Modeling Belief in Dynamic Systems, Part II: Revision and Update
The study of belief change has been an active area in philosophy and AI. In
recent years two special cases of belief change, belief revision and belief
update, have been studied in detail. In a companion paper (Friedman & Halpern,
1997), we introduce a new framework to model belief change. This framework
combines temporal and epistemic modalities with a notion of plausibility,
allowing us to examine the change of beliefs over time. In this paper, we show
how belief revision and belief update can be captured in our framework. This
allows us to compare the assumptions made by each method, and to better
understand the principles underlying them. In particular, it shows that Katsuno
and Mendelzon's notion of belief update (Katsuno & Mendelzon, 1991a) depends on
several strong assumptions that may limit its applicability in artificial
intelligence. Finally, our analysis allow us to identify a notion of minimal
change that underlies a broad range of belief change operations including
revision and update.Comment: See http://www.jair.org/ for other files accompanying this articl
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