Belief revision has been extensively studied in the framework of propositional logic, but just recently revision within fragments of propositional logic has gained attention. Hereby it is not only the belief set and the revision formula which are given within a certain language fragment, but also the result of the revision has to be located in the same fragment. So far, research in this direction has been mainly devoted to the Horn fragment of classical logic. In this work, we present a general approach to define new revision operators derived from known operators (as for instance, Satoh's and Dalal's revision operators), such that the result of the revision remains in the fragment under consideration. Our approach is not limited to the Horn case but applicable to any fragment of propositional logic where the models of the formulas are closed under a Boolean function. Thus we are able to uniformly treat cases as dual-Horn, Krom and affine formulas, as well.

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.

The QXOR-SAT problem is the quantified version of the satisfiability problem XOR-SAT in which the connective exclusive-or is used instead of the usual or. We study the phase transition associated with random QXOR-SAT instances. We give a description of this phase transition in the case of one alternation of quantifiers, thus performing an advanced practical and theoretical study on the phase transition of a quantified problem.

The QXOR-SAT problem is the quantified version of the satisfiability problem XOR-SAT in which the connective exclusive-or is used instead of the usual or. We study the phase transition associated with random QXOR-SAT instances. We give a description of this phase transition in the case of one alternation of quantifiers, thus performing an advanced practical and theoretical study on the phase transition of a quantified problem.