Decidability Under the Well-Founded Semantics
نویسندگان
چکیده
The well-founded semantics (WFS) for logic programs is one of the few major paradigms for closed-world reasoning. With the advent of the Semantic Web, it is being used as part of rule systems for ontology reasoning, and also investigated as to its usefulness as a semantics for hybrid systems featuring combined openand closed-world reasoning. Even in its most basic form, however, the WFS is undecidable. In fact, it is not even semi-decidable, which means that it is a theoretical impossibility that sound and complete reasoners for the WFS exist. Surprisingly, however, this matter has received next to no attention in research, although it has already been shown in 1995 by John Schlipf [1]. In this paper, we present several conditions under which query-answering under the well-founded semantics is decidable or semi-decidable. To the best of our knowledge, these are the very first results on such conditions.
منابع مشابه
A Sufficient Condition for Strong Equivalence Under the Well-Founded Semantics
We consider the problem of strong equivalence [1] under the infinite-valued semantics [2] (which is a purely model-theoretic version of the well-founded semantics). We demonstrate that two programs are now strongly equivalent if and only if they are logically equivalent under the infinite-valued logic of [2]. In particular, we show that for propositional programs, strong equivalence is decidabl...
متن کاملReconciling Well-Founded Semantics of DL-Programs and Aggregate Programs
Logic programs with aggregates and description logic programs (dl-programs) are two recent extensions to logic programming. In this paper, we study the relationships between these two classes of logic programs, under the well-founded semantics. The main result is that, under a satisfaction-preserving mapping from dl-atoms to aggregates, the well-founded semantics of dl-programs by Eiter et al.,...
متن کاملForgetting under the Well-Founded Semantics
Recently, the notion of forgetting has drawn considerable attention in the area of Knowledge Representation and Reasoning. The underlying idea is to discard a part of the knowledge base without affecting the derivations on, e.g., atoms that are not to be forgotten. Several recent papers consider forgetting under answer set semantics, but sometimes the well-founded semantics with data complexity...
متن کاملA Scheme for Weakened Negative Introspection in Autoepistemic Reasoning
A novel scheme for weakened negative introspection in au-toepistemic reasoning is proposed. The scheme is formulated proof-theoretically in terms of enumerations of formulae. The resulting sets of conclusions , cautious expansions, are a generalization of Moore style stable expansions such that each set of premises has a cautious expansion. A nitary characterization is provided for the cautious...
متن کاملThe Well-Founded Semantics of Cyclic Probabilistic Logic Programs: Meaning and Complexity
This paper investigates the properties of cyclic probabilistic normal logic programs, consisting of rules and a set of independent probabilistic facts, under the well-founded semantics. That is, we assume that for each fixed truth assignment for the probabilistic facts, the resulting normal logic program is interpreted through the well-founded semantics. We derive results concerning the complex...
متن کامل