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"Towards a Semantic Construction for Belief Base Contraction: Partial Meet vs Smooth Kernel" (Preliminary Report)

von Jandson S. Ribeiro

Abstract: We introduce novel classes of fully rational contraction operators for belief bases. These operators are founded on a plausibility relation on models, called tracks, that allow distinguishing between suitable and unsuitable models. We obtain two main representation theorems: the first one semantically characterizes the class of partial-meet operators, which are related to the rationality postulate of relevance; while the second one semantically characterizes the class of smooth kernel contraction operators, which are related to the postulates of core-retainment and relative closure. For the supplementary postulates (conjunction and intersection), we strengthen such operators by imposing the mirroring condition on the track relations. We consider logics that are both Tarskian and compact.

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