544,859 research outputs found
Extremal problems in logic programming and stable model computation
We study the following problem: given a class of logic programs C, determine
the maximum number of stable models of a program from C. We establish the
maximum for the class of all logic programs with at most n clauses, and for the
class of all logic programs of size at most n. We also characterize the
programs for which the maxima are attained. We obtain similar results for the
class of all disjunctive logic programs with at most n clauses, each of length
at most m, and for the class of all disjunctive logic programs of size at most
n. Our results on logic programs have direct implication for the design of
algorithms to compute stable models. Several such algorithms, similar in spirit
to the Davis-Putnam procedure, are described in the paper. Our results imply
that there is an algorithm that finds all stable models of a program with n
clauses after considering the search space of size O(3^{n/3}) in the worst
case. Our results also provide some insights into the question of
representability of families of sets as families of stable models of logic
programs
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
Stability and stable groups in continuous logic
We develop several aspects of local and global stability in continuous first
order logic. In particular, we study type-definable groups and genericity
Tight Logic Programs
This note is about the relationship between two theories of negation as
failure -- one based on program completion, the other based on stable models,
or answer sets. Francois Fages showed that if a logic program satisfies a
certain syntactic condition, which is now called ``tightness,'' then its stable
models can be characterized as the models of its completion. We extend the
definition of tightness and Fages' theorem to programs with nested expressions
in the bodies of rules, and study tight logic programs containing the
definition of the transitive closure of a predicate.Comment: To appear in Special Issue of the Theory and Practice of Logic
Programming Journal on Answer Set Programming, 200
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