Belief Update Within Propositional Fragments

Abstract

Belief change within the framework of fragments of propositional logic is one of the main and recent challenges in the knowledge representation research area. While previous research works focused on belief revision, belief merging, and belief contraction, the problem of belief update within fragments of classical logic has not been addressed so far. In the context of revision, it has been proposed to refine existing operators so that they operate within propositional fragments, and that the result of revision remains in the fragment under consideration. This approach is not restricted to the Horn fragment but also applicable to other propositional fragments like Krom and affine fragments. We generalize this notion of refinement to any belief change operator. We then focus on a specific belief change operation, namely belief update. We investigate the behavior of the refined update operators with respect to satisfaction of the KM postulates and highlight differences between revision and update in this context.

On Mixed Iterated Revisions

“…The analysis would not be obvious because underformulae include both disjunction and conjunction, which may result in a non-Horn and non-Krom formula. The Horn restriction has been studied in single-step revisions by Eiter and Gottlob [18], and has recently been considered as a contributor to the semantics of revision [14].…”

“…However, efficient solvers have been developed [4,2]. Restricting to a less expressive language [14] such as Horn logic may also reduce the complexity of the problem, as it is generally the case for one-step revisions [19,54,50,45], since satisfiability in this case can be solved efficiently. Some complexity results are proved: some imply the ones announced without proofs in a previous article [47], but extend them to the case of mixed sequences of revisions.…”

Belief contraction and erasure in fragments of propositional logic

“…A natural objective is to define rational refined belief change operators that satisfy expected rationality postulates. Contrary to the case of revision and update [6,11], the refined contraction (respectively, erasure) operators do not necessarily satisfy the basic postulates for contraction (respectively, erasure) operators. In order to encompass a wider class of refined belief change operators including contraction and erasure, we introduce a specific notion of refinement, called reasonable refinement.…”

“…Many studies focused on belief change within the framework of propositional logic fragments, particularly on belief revision [4,17,51,41,6], belief merging [7], belief update [11] and belief contraction [15,46,2,49,14,50]. However, as far as we know, research in belief contraction has been mainly devoted to the Horn fragment and belief erasure has attracted no attention.…”

“…The notion of refinement, initially defined for revision [6], was extended in [11] to any belief change operator defined from L × L to L where L denotes propositional logic. A refinement adapts a belief change operator defined in a propositional setting such that it can be applicable in a propositional fragment.…”