685 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
Super Logic Programs
The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful
nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper,
we specialize it to a class of theories called `super logic programs'. We argue
that these programs form a natural generalization of standard logic programs.
In particular, they allow disjunctions and default negation of arbibrary
positive objective formulas.
Our main results are two new and powerful characterizations of the static
semant ics of these programs, one syntactic, and one model-theoretic. The
syntactic fixed point characterization is much simpler than the fixed point
construction of the static semantics for arbitrary AELB theories. The
model-theoretic characterization via Kripke models allows one to construct
finite representations of the inherently infinite static expansions.
Both characterizations can be used as the basis of algorithms for query
answering under the static semantics. We describe a query-answering interpreter
for super programs which we developed based on the model-theoretic
characterization and which is available on the web.Comment: 47 pages, revised version of the paper submitted 10/200
Towards a unified theory of logic programming semantics: Level mapping characterizations of selector generated models
Currently, the variety of expressive extensions and different semantics
created for logic programs with negation is diverse and heterogeneous, and
there is a lack of comprehensive comparative studies which map out the
multitude of perspectives in a uniform way. Most recently, however, new
methodologies have been proposed which allow one to derive uniform
characterizations of different declarative semantics for logic programs with
negation. In this paper, we study the relationship between two of these
approaches, namely the level mapping characterizations due to [Hitzler and
Wendt 2005], and the selector generated models due to [Schwarz 2004]. We will
show that the latter can be captured by means of the former, thereby supporting
the claim that level mappings provide a very flexible framework which is
applicable to very diversely defined semantics.Comment: 17 page
Relating Weight Constraint and Aggregate Programs: Semantics and Representation
Weight constraint and aggregate programs are among the most widely used logic
programs with constraints. In this paper, we relate the semantics of these two
classes of programs, namely the stable model semantics for weight constraint
programs and the answer set semantics based on conditional satisfaction for
aggregate programs. Both classes of programs are instances of logic programs
with constraints, and in particular, the answer set semantics for aggregate
programs can be applied to weight constraint programs. We show that the two
semantics are closely related. First, we show that for a broad class of weight
constraint programs, called strongly satisfiable programs, the two semantics
coincide. When they disagree, a stable model admitted by the stable model
semantics may be circularly justified. We show that the gap between the two
semantics can be closed by transforming a weight constraint program to a
strongly satisfiable one, so that no circular models may be generated under the
current implementation of the stable model semantics. We further demonstrate
the close relationship between the two semantics by formulating a
transformation from weight constraint programs to logic programs with nested
expressions which preserves the answer set semantics. Our study on the
semantics leads to an investigation of a methodological issue, namely the
possibility of compact representation of aggregate programs by weight
constraint programs. We show that almost all standard aggregates can be encoded
by weight constraints compactly. This makes it possible to compute the answer
sets of aggregate programs using the ASP solvers for weight constraint
programs. This approach is compared experimentally with the ones where
aggregates are handled more explicitly, which show that the weight constraint
encoding of aggregates enables a competitive approach to answer set computation
for aggregate programs.Comment: To appear in Theory and Practice of Logic Programming (TPLP), 2011.
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