1,552 research outputs found
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
in a program, an objective literal along with rules that ensure
that will be true if and only if 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
SLT-Resolution for the Well-Founded Semantics
Global SLS-resolution and SLG-resolution are two representative mechanisms
for top-down evaluation of the well-founded semantics of general logic
programs. Global SLS-resolution is linear for query evaluation but suffers from
infinite loops and redundant computations. In contrast, SLG-resolution resolves
infinite loops and redundant computations by means of tabling, but it is not
linear. The principal disadvantage of a non-linear approach is that it cannot
be implemented using a simple, efficient stack-based memory structure nor can
it be easily extended to handle some strictly sequential operators such as cuts
in Prolog.
In this paper, we present a linear tabling method, called SLT-resolution, for
top-down evaluation of the well-founded semantics. SLT-resolution is a
substantial extension of SLDNF-resolution with tabling. Its main features
include: (1) It resolves infinite loops and redundant computations while
preserving the linearity. (2) It is terminating, and sound and complete w.r.t.
the well-founded semantics for programs with the bounded-term-size property
with non-floundering queries. Its time complexity is comparable with
SLG-resolution and polynomial for function-free logic programs. (3) Because of
its linearity for query evaluation, SLT-resolution bridges the gap between the
well-founded semantics and standard Prolog implementation techniques. It can be
implemented by an extension to any existing Prolog abstract machines such as
WAM or ATOAM.Comment: Slight modificatio
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