Embedding Defeasible Logic into Logic Programming

Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches. In this paper we establish close links to known semantics of logic programs. In particular, we give a translation of a defeasible theory D into a meta-program P(D). We show that under a condition of decisiveness, the defeasible consequences of D correspond exactly to the sceptical conclusions of P(D) under the stable model semantics. Without decisiveness, the result holds only in one direction (all defeasible consequences of D are included in all stable models of P(D)). If we wish a complete embedding for the general case, we need to use the Kunen semantics of P(D), instead.Comment: To appear in Theory and Practice of Logic Programmin

Embedding Defeasible Logic in Logic Progamming

Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches. In this paper we establish close links to known semantics of logic programs. In particular, we give a translation of a defeasible theory D into a meta-program P(D). We show that under a condition of decisiveness, the defeasible consequences of D correspond exactly to the sceptical conclusions of P(D) under the stable model semantics. Without decisiveness, the result holds only in one direction (all defeasible consequences of D are included in all stable models of P(D)). If we wish a complete embedding for the general case, we need to use the Kunen semantics of P(D), instead

An analysis of the computational complexity of DeLP through game semantics

Defeasible Logic Programming (DeLP) is a suitable tool for knowledge representation and reasoning. Its operational semantics is based on a dialectical analysis where arguments for and against a literal interact in order to determine whether this literal is believed by a reasoning agent. The semantics GS is a declarative trivalued game-based semantics for DeLP that is sound and complete for DeLP operational semantics. Complexity theory has become an important tool for comparing different formalism and for helping to improve implementations whenever is possible. For these reasons, it is important to investigate the computational complexity and expressive power of DeLP. In this paper we present a complexity analysis of DeLP through game-semantics GS. In particular, we have determined that computing rigorous consequences is P-complete and that the decision problem “a set of defeasible rules is an argument for a literal under a de.l.p.” is in P.VI Workshop de Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

An analysis of the computational complexity of DeLP through game semantics

Defeasible Logic Programming (DeLP) is a suitable tool for knowledge representation and reasoning. Its operational semantics is based on a dialectical analysis where arguments for and against a literal interact in order to determine whether this literal is believed by a reasoning agent. The semantics GS is a declarative trivalued game-based semantics for DeLP that is sound and complete for DeLP operational semantics. Complexity theory has become an important tool for comparing different formalism and for helping to improve implementations whenever is possible. For these reasons, it is important to investigate the computational complexity and expressive power of DeLP. In this paper we present a complexity analysis of DeLP through game-semantics GS. In particular, we have determined that computing rigorous consequences is P-complete and that the decision problem “a set of defeasible rules is an argument for a literal under a de.l.p.” is in P.VI Workshop de Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

Non-monotonic reasoning with normative conflicts in multi-agent deontic logic

We present two multi-agent deontic logics that consistently accommodate various types of normative conflicts. Its language features modal operators for obligation and permission, and for the realization of individual and collective actions. The logic is non-classical since it makes use of a paraconsistent and paracomplete negation connective. Moreover, it is non-monotonic due to its definition within the adaptive logics framework for defeasible reasoning. The logic is equipped with a defeasible proof theory and semantics

A flexible framework for defeasible logics

Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several logics and, when necessary, combine the representations. In general, such an approach results in a very difficult problem of combination. However, if we can choose the logics from a uniform framework then the problem of combining them is greatly simplified. In this paper, we develop such a framework for defeasible logics. It supports all defeasible logics that satisfy a strong negation principle. We use logic meta-programs as the basis for the framework.Comment: Proceedings of 8th International Workshop on Non-Monotonic Reasoning, April 9-11, 2000, Breckenridge, Colorad