Genes and Ant for Defaults Logic

Default Logic and Logic Programming with stable model semantics are recognized as powerful frameworks for incomplete information representation. Their expressive power are suitable for non monotonic reasoning, but the counterpart is their very high level of theoretical complexity. The purpose of this paper is to show how heuristics issued from combinatorial optimization and operation research can be used to built non monotonic reasonning systems

Combining Heuristics for Default Logic Reasoning Systems

In Artificial Intelligence, Default Logic is recognized as a powerful framework for knowledge representation when one has to deal with incomplete information. Its expressive power is suitable for nonmonotonic reasoning, but the counterpart is its very high level of theoretical complexity. Today, some operational systems are able to deal with real world applications. However finding a default logic extension in a practical way is not yet possible in whole generality. This paper shows how modern heuristics such as genetic algorithms and local search techniques can be used and combined to build an automated default reasoning system. We give a general description of the required basic components and we exhibit experimental result

Expressive Non-Monotonic Description Logics Based on Circumscription

Recent applications of description logics (DLs) strongly suggest the integration of non-monotonic features into DLs, with particular attention to defeasible inheritance. However, the existing non-monotonic extensions of DLs are usually based on default logic or autoepistemic logic, and have to be seriously restricted in expressive power to preserve the decidability of reasoning. In particular, such DLs allow the modelling of defeasible inheritance only in a very restricted form, where non-monotonic reasoning is limited to individuals that are explicitly identified by constants in the knowledge base. In this paper, we consider non-monotonic extensions of expressive DLs based on circumscription. We prove that reasoning in such DLs is decidable even without the usual, strong restrictions in expressive power. We pinpoint the exact computational complexity of reasoning as complete for NPNEXP and NEXPNP, depending on whether or not the number of minimized and fixed predicates is assumed to be bounded by a constant. These results assume that only concept names (and no role names) can be minimized and fixed during minimization. On the other hand, we show that fixing role names during minimization makes reasoning undecidable

Heuristics for a Default Logic Reasoning System

In Artificial Intelligence, Default Logic is recognized as a powerful framework for knowledge representation when one has to deal with incomplete information. Its expressive power is suitable for non monotonic reasoning, but the counterpart is its very high level of theoretical complexity. Today, some operational systems are able to deal with real world applications. However, finding a default logic extension in a practical way is not yet possible in whole generality. This paper which is an extended version of18 shows how heuristics such as Genetic Algorithms and Local Search techniques can be used and combined to build an automated default reasoning system. We give a general description of the required basic components and we exhibit experimental results.

Abduction in Well-Founded Semantics and Generalized Stable Models

Abductive logic programming offers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming offers a computational mechanism that provides a level of declarativity superior to that of Prolog, and which has supported successful applications in fields such as parsing, program analysis, and model checking. In this paper we show how to use tabled logic programming to evaluate queries to abductive frameworks with integrity constraints when these frameworks contain both default and explicit negation. The result is the ability to compute abduction over well-founded semantics with explicit negation and answer sets. Our approach consists of a transformation and an evaluation method. The transformation adjoins to each objective literal $O$ in a program, an objective literal $not(O)$ along with rules that ensure that $not(O)$ will be true if and only if $O$ is false. We call the resulting program a {\em dual} program. The evaluation method, \wfsmeth, then operates on the dual program. \wfsmeth{} is sound and complete for evaluating queries to abductive frameworks whose entailment method is based on either the well-founded semantics with explicit negation, or on answer sets. Further, \wfsmeth{} is asymptotically as efficient as any known method for either class of problems. In addition, when abduction is not desired, \wfsmeth{} operating on a dual program provides a novel tabling method for evaluating queries to ground extended programs whose complexity and termination properties are similar to those of the best tabling methods for the well-founded semantics. A publicly available meta-interpreter has been developed for \wfsmeth{} using the XSB system.Comment: 48 pages; To appear in Theory and Practice in Logic Programmin