Iterated Syntax-Based Revision in a Nonmonotonic Setting

Abstract

Various approaches to belief revision have been proposed this last decade. Most of them have been investigated from a knowledge-level theoretical perspective [Newell, 1982], mainly. Despite a few noticeable exceptions (e.g. [Papini, 1991] [Nebel, 1992] [Eiter and Gottlob, 1992] [Liberatore and Schaerf, 1996]), their computational counterparts have rarely been considered. Worse, due to worst case complexity results, they are often believed to be intractable when large-scale applications are addressed. However, recent impressive empirical progress in propositional reasoning and search [Selman et al., 1997] does open real computational perspectives for syntax-based approaches to belief revision with respect to large applications. Also, many efforts have been devoted to establish formal connections between nonmonotonic logics and belief revision (see e.g. [del Val, 1984] [Makinson and Gärdenfors, 1991] [Moinard, 1994] [Liberatore and Schaerf, 1995]). In this paper, a knowlegel engineering-motivated approach to belief revision is adopted, showing that belief revision and nonmonotonic logics are not only two sides of the same coin [Gärdenfors, 1992] but that they can play useful synergetic roles in a unified framework that proves empirically computationally viable. More precisely, a two-steps policy to syntax-based revision of inconsistent beliefs is proposed. On the one hand, nonmonotonic ingredients are provided within a belief representation language giving rise to a gain of expressiveness, allowing a careful knowledge engineer to avoid many future inconsistencies that would occur if a standard deductive representation and inference of beliefs were selected. Inconsistencies that are not forecast and prevented in this way are then the object of a syntax-based belief revision process. In this respect, we can envision a whole family of syntax-based revision approaches: from a full-meet cautious one that weakens each formula in each minimally inconsistent subbase to regain consistency, to a maxichoice change policy that just weakens one smallest subset of formulas to restore consistency. In this paper, an empirically viable computational technique for the first approach is proposed. It makes use of a specific heuristic in the trace of local search techniques to check (in)consistency. Interestingly enough, it is shown that the nonmonotonic ingredients do not significantly affect the computational complexity results with respect to the revision process, neither from a worst case point of view, nor from an empirical one.