24 research outputs found
SLDNFA-system
The SLDNFA-system results from the LP+ project at the K.U.Leuven, which
investigates logics and proof procedures for these logics for declarative
knowledge representation. Within this project inductive definition logic
(ID-logic) is used as representation logic. Different solvers are being
developed for this logic and one of these is SLDNFA. A prototype of the system
is available and used for investigating how to solve efficiently problems
represented in ID-logic.Comment: 6 pages conference:NMR2000, special track on System descriptions and
demonstratio
Logic Programming for Describing and Solving Planning Problems
A logic programming paradigm which expresses solutions to problems as stable
models has recently been promoted as a declarative approach to solving various
combinatorial and search problems, including planning problems. In this
paradigm, all program rules are considered as constraints and solutions are
stable models of the rule set. This is a rather radical departure from the
standard paradigm of logic programming. In this paper we revisit abductive
logic programming and argue that it allows a programming style which is as
declarative as programming based on stable models. However, within abductive
logic programming, one has two kinds of rules. On the one hand predicate
definitions (which may depend on the abducibles) which are nothing else than
standard logic programs (with their non-monotonic semantics when containing
with negation); on the other hand rules which constrain the models for the
abducibles. In this sense abductive logic programming is a smooth extension of
the standard paradigm of logic programming, not a radical departure.Comment: 8 pages, no figures, Eighth International Workshop on Nonmonotonic
Reasoning, special track on Representing Actions and Plannin
Problem solving in ID-logic with aggregates: some experiments
The goal of the LP+ project at the K.U.Leuven is to design an expressive
logic, suitable for declarative knowledge representation, and to develop
intelligent systems based on Logic Programming technology for solving
computational problems using the declarative specifications. The ID-logic is an
integration of typed classical logic and a definition logic. Different
abductive solvers for this language are being developed. This paper is a report
of the integration of high order aggregates into ID-logic and the consequences
on the solver SLDNFA.Comment: 9 pages conference: NMR2000, special track on abductive reasonin
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
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
A Tarskian Informal Semantics for Answer Set Programming
In their seminal papers on stable model semantics, Gelfond and Lifschitz introduced ASP by casting programs as epistemic theories, in which rules represent statements about the knowledge of a rational
agent. To the best of our knowledge, theirs is still the only published systematic account of the intuitive meaning of rules and programs under the stable semantics. In current ASP practice, however, we find numerous applications in which rational agents no longer seem to play any role. Therefore, we propose here an alternative explanation of the intuitive meaning of ASP programs, in which they are not viewed as statements about an agent\u27s beliefs, but as objective statements about the world. We argue that this view is more natural for a large part of current ASP practice, in particular the so-called Generate-Define-Test programs
Epistemic Foundation of Stable Model Semantics
Stable model semantics has become a very popular approach for the management
of negation in logic programming. This approach relies mainly on the closed
world assumption to complete the available knowledge and its formulation has
its basis in the so-called Gelfond-Lifschitz transformation.
The primary goal of this work is to present an alternative and
epistemic-based characterization of stable model semantics, to the
Gelfond-Lifschitz transformation. In particular, we show that stable model
semantics can be defined entirely as an extension of the Kripke-Kleene
semantics. Indeed, we show that the closed world assumption can be seen as an
additional source of `falsehood' to be added cumulatively to the Kripke-Kleene
semantics. Our approach is purely algebraic and can abstract from the
particular formalism of choice as it is based on monotone operators (under the
knowledge order) over bilattices only.Comment: 41 pages. To appear in Theory and Practice of Logic Programming
(TPLP