Solving logic program conflict through strong and weak forgettings

Abstract

We consider how to forget a set of atoms in a logic program. Intuitively, when a set of atoms is forgotten from a logic program, all atoms in the set should be eliminated from this program in some way, and other atoms related to them in the program might also be affected. We define notions of strong and weak forgettings in logic programs to capture such intuition and reveal their close connections to the notion of forgetting in classical propositional theories. Based on these notions, we then propose a framework for conflict solving in logic programs, which is general enough to represent many important conflict solving problems. We also study some essential semantic and computational properties in relation to strong and weak forgettings and conflict solving in our framework.

Merging and Aligning Ontologies in dl-Programs

“…In this paper we have generalized dl-programs by allowing multiple knowledge bases and then accordingly, defined the answer set semantics for the dl-programs. The notion of forgetting has been proved an extremely useful technique for updating knowledge bases, constraint problem solving and query answering [12,17,18]. In this paper we have imported the notion of forgetting into dl-programs.…”

Introspective Forgetting

“…Baral and Zhang joined this battleground for more explicit operators for knowledge and belief with their (Baral and Zhang, 2005), wherein the result of an agent forgetting a variable results in her (explicit) ignorance of that variable's value, and in (Zhang and Zhou, 2008), in progress, Zhang and Zhou make an original and interesting backtrack to the ideas of (Lin and Reiter, 1994) by suggesting bisimulation invariance except for the forgotten variable, in order to model forgetting. Forgetting has been generalized to logic programs in Zhang et al, 2005;Eiter and Wang, 2006) and to description logics in (Zhao et al, 2007). Forgetting of (abstracting from) actions in planning has been investigated in (Erdem and Ferraris, 2007).…”

Forgetting for Defeasible Logic

“…Informally, given a knowledge base, we may wish to forget about (or discard) some redundant parts (such as atoms, predicates, concepts, etc) but still preserve the consequences for certain forms of reasoning. Forgetting has been introduced in many formalisms for knowledge representation, for instance, in propositional logic [17,18], first-order logic [19,31], modal logic [25,14,30], description logic [28,27,16], and logic programming [7,26,29]. The theory of forgetting has also been fruitfully applied in various contexts, e.g.…”