Dalal's Revision without Hamming Distance

International audienceA well known strategy for belief revision is the use of an operator which takes as input a belief base and formula and outputs a new consistent revised belief base. Many operators require additional information such as epistemic entrenchment relations, system of spheres, faithful orderings, subformulae relation, etc. However, in many applications this extra information does not exist and all beliefs have to be equally considered. Other operators that can do without background information are dependent on the syntax. Among the few operators that possess both kinds of independence: of extra information and of the syntax, Dalal’s operator is the most outstanding. Dalal’s revision moves from the models of the base to the models of the input formula which are closest in terms of Hamming distance. A drawback of Dalal’s approach is that it fails when faced with inconsistent belief bases. This paper proposes a new method for computing Dalal’s revision that avoids the computation of belief bases models. We propose a new distance between formulae based on distances between terms of formulae in DNF and a revision operator based on these distances. The proposed operator produces Dalal’s equivalent results when the belief base and new input are both consistent. Moreover, this new operator is able to handle inconsistent belief bases. We also analyze several properties of the new operator. While the input belief base and formula need a compilation to DNF, the operator meets desirable properties making the approach suitable for implementation

Incremental Recompilation of Knowledge

Approximating a general formula from above and below by Horn formulas (its Horn envelope and Horn core, respectively) was proposed by Selman and Kautz (1991, 1996) as a form of ``knowledge compilation,'' supporting rapid approximate reasoning; on the negative side, this scheme is static in that it supports no updates, and has certain complexity drawbacks pointed out by Kavvadias, Papadimitriou and Sideri (1993). On the other hand, the many frameworks and schemes proposed in the literature for theory update and revision are plagued by serious complexity-theoretic impediments, even in the Horn case, as was pointed out by Eiter and Gottlob (1992), and is further demonstrated in the present paper. More fundamentally, these schemes are not inductive, in that they may lose in a single update any positive properties of the represented sets of formulas (small size, Horn structure, etc.). In this paper we propose a new scheme, incremental recompilation, which combines Horn approximation and model-based updates; this scheme is inductive and very efficient, free of the problems facing its constituents. A set of formulas is represented by an upper and lower Horn approximation. To update, we replace the upper Horn formula by the Horn envelope of its minimum-change update, and similarly the lower one by the Horn core of its update; the key fact which enables this scheme is that Horn envelopes and cores are easy to compute when the underlying formula is the result of a minimum-change update of a Horn formula by a clause. We conjecture that efficient algorithms are possible for more complex updates.Comment: See http://www.jair.org/ for any accompanying file

09351 Abstracts Collection -- Information processing, rational belief change and social interaction

From 23.08. to 27.08.2009, the Dagstuhl Seminar 09351 ``Information processing, rational belief change and social interaction \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Dalal's Revision without Hamming Distance

A well known strategy for belief revision is the use of an operator which takes as input a belief base and formula and outputs a new consistent revised belief base. Many operators require additional information such as epistemic entrenchment relations, system of spheres, faithful orderings, subformulae relation, etc. However, in many applications this extra information does not exist and all beliefs have to be equally considered. Other operators that can do without background information are dependent on the syntax. Among the few operators that possess both kinds of independence: of extra information and of the syntax, Dalal’s operator is the most outstanding. Dalal’s revision moves from the models of the base to the models of the input formula which are closest in terms of Hamming distance. A drawback of Dalal’s approach is that it fails when faced with inconsistent belief bases. This paper proposes a new method for computing Dalal’s revision that avoids the computation of belief bases models. We propose a new distance between formulae based on distances between terms of formulae in DNF and a revision operator based on these distances. The proposed operator produces Dalal’s equivalent results when the belief base and new input are both consistent. Moreover, this new operator is able to handle inconsistent belief bases. We also analyze several properties of the new operator. While the input belief base and formula need a compilation to DNF, the operator meets desirable properties making the approach suitable for implementation