: This paper is concerned with the construction of a base contraction (revision) operation such that the theory contraction (revision) operation generated by it will be fully AGM-rational. It is shown that the theory contraction operation generated by Fuhrmann's minimal base contraction operation, even under quite strong restrictions, fails to satisfy the "supplementary postulates" of belief contraction. Finally Fuhrmann's construction is appropriately modified so as to yield the desired properties. The new construction may be described as involving a modification of safe (base) contraction so as to make it maxichoice. Descriptors: belief, change, contraction, revision, base, theory. We often change our beliefs. We learn new things, occasionally things that conflict with our current beliefs. On such occasions new beliefs replace the old ones. It is as if this process is completed in two steps: (1) first we identify and throw out the beliefs that conflict with the new information and t...

This paper presents a general, consistency-based framework for expressing belief change.

The paper introduces ten open problems in belief revision theory, related to the representation of the belief state, to different notions of degrees of belief, and to the nature of change operations. It is argued that these problems are all issues in philosopical logic, in the strong sense of requiring inputs from both logic and philosophy for their solution. 1

Abstract This paper aims to extend the AGM theory of belief revision to accommodate infinitary belief change. We generalize the AGM theory both in axiomatization and modeling. We show that most properties of the AGM belief change operations are preserved by the generalized operations whereas the infinitary belief change operations have their special properties. We prove that the extended axiomatic system for the generalized belief change operators with a Limit Postulate properly specifies infinite belief change. This framework forms a base for first-order belief revision and the theory of revising a belief state by a belief state.

Heinrich Wansing Dresden University of Technology The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is derived that all truths are, in fact, known. Nevertheless, the solution o#ered is in the spirit of the constructivist attitude usually maintained by defenders of the anti-realist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete.

We describe COBA 2.0, an implementation of a consistency-based framework for expressing belief change, focusing here on revision and contraction, with the possible incorporation of integrity constraints. This general framework was first proposed in [1]; following a review of this work, we present COBA 2.0’s high-level algorithm, work through several examples, and describe our experiments. A distinguishing feature of COBA 2.0 is that it builds on SATtechnology by using a module comprising a state-of-the-art SAT-solver for consistency checking. As well, it allows for the simultaneous specification of revision, multiple contractions, along with integrity constraints, with respect to a given knowledge base.

The ability to change one’s beliefs consistently is essential for sound reasoning in a world where the new information one acquires may invalidate or augment one’s current beliefs. Belief revision is the process wherein an agent modifies its beliefs to incorporate the new information received, and knowledge base merging the process wherein the agent is given two or more knowledge bases to merge. We present a binary decision diagram (BDD)- based implementation of Delgrande and Schaub’s consistency-based belief change framework. Our system focuses on knowledge base merging with the possible incorporation of integrity constraints, using a BDD solver for consistency checking. We show that the result of merging finite knowledge bases can be represented as a finite formula, and that merging can be streamlined algorithmically by restricting attention to a subset of the vocabulary of the propositional formulas involved. Experimental results and comparisons with related systems are also given.