Belief Update Within Propositional Fragments

Recently, belief change within the framework of fragments of propositional logic has gained attention. Previous works focused on belief revision, belief merging, and on belief contraction in the Horn fragment. The problem of belief update within the framework of fragments of propositional logic has been neglected so far. In the same spirit as a previous extension of belief revision to propositional fragments, we propose a general approach to define new update operators derived from existing ones such that the result of update remains in the fragment under consideration. Our approach is not limited to the Horn fragment but applicable to many fragments of propositional logic, like Horn, Krom and affine fragments. We study the logical properties of the proposed operators in terms of the KM’s postulates satisfaction and highlight differences between revision and update in this context.

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