59,710 research outputs found
Three-valued completion for abductive logic programs
AbstractIn this paper, we propose a three-valued completion semantics for abductive logic programs, which solves some problems associated with the Console et al. two-valued completion semantics. The semantics is a generalization of Kunen's completion semantics for general logic programs, which is known to correspond very well to a class of effective proof procedures for general logic programs. Secondly, we propose a proof procedure for abductive logic programs, which is a generalization of a proof procedure for general logic programs based on constructive negation. This proof procedure is sound and complete with respect to the proposed semantics. By generalizing a number of results on general logic programs to the class of abductive logic programs, we present further evidence for the idea that limited forms of abduction can be added quite naturally to general logic programs
Logic Programming with Default, Weak and Strict Negations
This paper treats logic programming with three kinds of negation: default,
weak and strict negations. A 3-valued logic model theory is discussed for logic
programs with three kinds of negation. The procedure is constructed for
negations so that a soundness of the procedure is guaranteed in terms of
3-valued logic model theory.Comment: 14 pages, to appear in Theory and Practice of Logic Programming
(TPLP
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
Ultimate approximations in nonmonotonic knowledge representation systems
We study fixpoints of operators on lattices. To this end we introduce the
notion of an approximation of an operator. We order approximations by means of
a precision ordering. We show that each lattice operator O has a unique most
precise or ultimate approximation. We demonstrate that fixpoints of this
ultimate approximation provide useful insights into fixpoints of the operator
O.
We apply our theory to logic programming and introduce the ultimate
Kripke-Kleene, well-founded and stable semantics. We show that the ultimate
Kripke-Kleene and well-founded semantics are more precise then their standard
counterparts We argue that ultimate semantics for logic programming have
attractive epistemological properties and that, while in general they are
computationally more complex than the standard semantics, for many classes of
theories, their complexity is no worse.Comment: This paper was published in Principles of Knowledge Representation
and Reasoning, Proceedings of the Eighth International Conference (KR2002
- …