747 research outputs found
Answer Sets for Logic Programs with Arbitrary Abstract Constraint Atoms
In this paper, we present two alternative approaches to defining answer sets
for logic programs with arbitrary types of abstract constraint atoms (c-atoms).
These approaches generalize the fixpoint-based and the level mapping based
answer set semantics of normal logic programs to the case of logic programs
with arbitrary types of c-atoms. The results are four different answer set
definitions which are equivalent when applied to normal logic programs. The
standard fixpoint-based semantics of logic programs is generalized in two
directions, called answer set by reduct and answer set by complement. These
definitions, which differ from each other in the treatment of
negation-as-failure (naf) atoms, make use of an immediate consequence operator
to perform answer set checking, whose definition relies on the notion of
conditional satisfaction of c-atoms w.r.t. a pair of interpretations. The other
two definitions, called strongly and weakly well-supported models, are
generalizations of the notion of well-supported models of normal logic programs
to the case of programs with c-atoms. As for the case of fixpoint-based
semantics, the difference between these two definitions is rooted in the
treatment of naf atoms. We prove that answer sets by reduct (resp. by
complement) are equivalent to weakly (resp. strongly) well-supported models of
a program, thus generalizing the theorem on the correspondence between stable
models and well-supported models of a normal logic program to the class of
programs with c-atoms. We show that the newly defined semantics coincide with
previously introduced semantics for logic programs with monotone c-atoms, and
they extend the original answer set semantics of normal logic programs. We also
study some properties of answer sets of programs with c-atoms, and relate our
definitions to several semantics for logic programs with aggregates presented
in the literature
Query-Answer Causality in Databases: Abductive Diagnosis and View-Updates
Causality has been recently introduced in databases, to model, characterize
and possibly compute causes for query results (answers). Connections between
query causality and consistency-based diagnosis and database repairs (wrt.
integrity constrain violations) have been established in the literature. In
this work we establish connections between query causality and abductive
diagnosis and the view-update problem. The unveiled relationships allow us to
obtain new complexity results for query causality -the main focus of our work-
and also for the two other areas.Comment: To appear in Proc. UAI Causal Inference Workshop, 2015. One example
was fixe
Properties and Applications of Programs with Monotone and Convex Constraints
We study properties of programs with monotone and convex constraints. We
extend to these formalisms concepts and results from normal logic programming.
They include the notions of strong and uniform equivalence with their
characterizations, tight programs and Fages Lemma, program completion and loop
formulas. Our results provide an abstract account of properties of some recent
extensions of logic programming with aggregates, especially the formalism of
lparse programs. They imply a method to compute stable models of lparse
programs by means of off-the-shelf solvers of pseudo-boolean constraints, which
is often much faster than the smodels system
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