A preliminary study of computational complexity in non-monotonic reasoning

In this work we analyze existing complexity results in the area of non-monotonic reasoning in general and argumentation in particular. Even though the area of argumentation is based on solid theoretical foundations, its main problems rely on the computational complexity of the system that have so far been developed. In order to use argumentation in real time scenarios we must find an implementation with a reasonable response time. Complexity analysis of argument systems is an indispensable tool for addressing this taks. We expect that the development of this research line will result in a general analysis of the issues in complexity of argument systems, leading to an efficient implementation of a particular formalism, observation-based defeasible logic programming, that could be integrated in an intelligent agent architecture.Eje: Inteligencia artificialRed de Universidades con Carreras en Informática (RedUNCI

The Complexity of Reasoning for Fragments of Default Logic

Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified the complexity of the extension existence problem for propositional default logic as \SigmaPtwo-complete, and the complexity of the credulous and skeptical reasoning problem as SigmaP2-complete, resp. PiP2-complete. Additionally, he investigated restrictions on the default rules, i.e., semi-normal default rules. Selman made in 1992 a similar approach with disjunction-free and unary default rules. In this paper we systematically restrict the set of allowed propositional connectives. We give a complete complexity classification for all sets of Boolean functions in the meaning of Post's lattice for all three common decision problems for propositional default logic. We show that the complexity is a hexachotomy (SigmaP2-, DeltaP2-, NP-, P-, NL-complete, trivial) for the extension existence problem, while for the credulous and skeptical reasoning problem we obtain similar classifications without trivial cases.Comment: Corrected versio

The Complexity of Reasoning for Fragments of Autoepistemic Logic

Autoepistemic logic extends propositional logic by the modal operator L. A formula that is preceded by an L is said to be "believed". The logic was introduced by Moore 1985 for modeling an ideally rational agent's behavior and reasoning about his own beliefs. In this paper we analyze all Boolean fragments of autoepistemic logic with respect to the computational complexity of the three most common decision problems expansion existence, brave reasoning and cautious reasoning. As a second contribution we classify the computational complexity of counting the number of stable expansions of a given knowledge base. To the best of our knowledge this is the first paper analyzing the counting problem for autoepistemic logic

Where Fail-Safe Default Logics Fail

Reiter's original definition of default logic allows for the application of a default that contradicts a previously applied one. We call failure this condition. The possibility of generating failures has been in the past considered as a semantical problem, and variants have been proposed to solve it. We show that it is instead a computational feature that is needed to encode some domains into default logic

A Default Logic Patch for Default Logic

International audienceThis paper is about the fusion of multiple information sources represented using default logic. More precisely, the focus is on solving the problem that occurs when the standard-logic knowledge parts of the sources are contradictory, as default theories trivialize in this case. To overcome this problem, it is shown that replacing each formula belonging to Minimally Unsatisfiable Subformulas by a corresponding supernormal default allows appealing features. Moreover, it is investigated how these additional defaults interact with the initial defaults of the theory. Interestingly, this approach allows us to handle the problem of default theories containing inconsistent standard-logic knowledge, using the default logic framework itself

Corriger la Logique des Défauts par la Logique des Défauts

National audienceCe papier se situe dans le contexte de la fusion de sources d'information représentées à l'aide de la logique des défauts. Plus précisément, celui-ci se focalise sur la résolution du problème apparaissant quand les connaissances classiques des sources sont contradictoires, ayant pour effet de rendre triviale la théorie avec défauts résultante. Pour outre-passer ce problème, il est montré que, remplacer chaque formule appartenant aux sous-ensembles minimaux inconsistants (MUSes) de la réunion des connaissances classiques des sources par une règle de défaut super-normale correspondante, présente un comportement intéressant. De plus, il est examiné comment ces règles de défaut supplémentaires interagissent avec les règles de défaut initiales de la théorie. Chose intéressante, cette approche nous permet de manier le problème de théories avec défauts contenant des connaissances classiques contradictoires, en utilisant le cadre de la logique des défauts lui-même

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