Semantic Constructions for Belief Base Contraction: Partial Meet vs Smooth Kernel

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 three main representation theorems: the first one semantically characterises the class of partial-meet operators, which are related to the rationality postulate of relevance; while the second one semantically characterises the class of smooth kernel contraction operators, which are related to the postulates of core-retainment and relative closure. The third representation theorem semantically characterises the supplementary postulates (conjunction and intersection). We consider logics that are both Tarskian and compact.