Knowledge Compilation of Logic Programs Using Approximation Fixpoint Theory

To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 2015 Recent advances in knowledge compilation introduced techniques to compile \emph{positive} logic programs into propositional logic, essentially exploiting the constructive nature of the least fixpoint computation. This approach has several advantages over existing approaches: it maintains logical equivalence, does not require (expensive) loop-breaking preprocessing or the introduction of auxiliary variables, and significantly outperforms existing algorithms. Unfortunately, this technique is limited to \emph{negation-free} programs. In this paper, we show how to extend it to general logic programs under the well-founded semantics. We develop our work in approximation fixpoint theory, an algebraical framework that unifies semantics of different logics. As such, our algebraical results are also applicable to autoepistemic logic, default logic and abstract dialectical frameworks

Ordered completion for first-order logic programs on finite structures

In this paper, we propose a translation from normal first-order logic programs under the answer set semantics to first-order theories on finite structures. Specifically, we introduce o dered completions which are modifications of Clark's con pletions with some extra predicates added to keep track of the derivation order, and show that on finite structures, classic; models of the ordered-completion of a normal logic program correspond exactly to the answer sets (stable models) of tre logic program. Copyright © 2010, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved

Ordered completion for first-order logic programs on finite structures

In this paper, we propose a translation from normal first-order logic programs under the stable model semantics to first-order sentences on finite structures. The translation is done through, what we call, ordered completion which is a modification of Clark's completion with some auxiliary predicates added to keep track of the derivation order. We show that, on finite structures, classical models of the ordered completion of a normal logic program correspond exactly to the stable models of the program. We also extend this result to normal programs with constraints and choice rules. From a theoretical viewpoint, this work clarifies the relationships between normal logic programming under the stable model semantics and classical first-order logic. It follows that, on finite structures, every normal program can be defined by a first-order sentence if new predicates are allowed. This is a tight result as not every normal logic program can be defined by a first-order sentence if no extra predicates are allowed or when infinite structures are considered. Furthermore, we show that the result cannot be extended to disjunctive logic programs, assuming that NP≠coNP. From a practical viewpoint, this work leads to a new type of ASP solver by grounding on a program's ordered completion instead of the program itself. We report on a first implementation of such a solver based on several optimization techniques. Our experimental results show that our solver compares favorably to other major ASP solvers on the Hamiltonian Circuit program, especially on large domains. © 2011 Elsevier B.V. All rights reserved

Ordered completion for first-order logic programs on finite structures

In this paper, we propose a translation from normal first-order logic programs under the answer set semantics to first-order theories on finite structures. Specifically, we introduce ordered completions which are modifications of Clark's completions with some extra predicates added to keep track of the derivation order, and show that on finite structures, classic; models of the ordered-completion of a normal logic program correspond exactly to the answer sets (stable models) of the logic program