6,654 research outputs found
A Common View on Strong, Uniform, and Other Notions of Equivalence in Answer-Set Programming
Logic programming under the answer-set semantics nowadays deals with numerous
different notions of program equivalence. This is due to the fact that
equivalence for substitution (known as strong equivalence) and ordinary
equivalence are different concepts. The former holds, given programs P and Q,
iff P can be faithfully replaced by Q within any context R, while the latter
holds iff P and Q provide the same output, that is, they have the same answer
sets. Notions in between strong and ordinary equivalence have been introduced
as theoretical tools to compare incomplete programs and are defined by either
restricting the syntactic structure of the considered context programs R or by
bounding the set A of atoms allowed to occur in R (relativized equivalence).For
the latter approach, different A yield properly different equivalence notions,
in general. For the former approach, however, it turned out that any
``reasonable'' syntactic restriction to R coincides with either ordinary,
strong, or uniform equivalence. In this paper, we propose a parameterization
for equivalence notions which takes care of both such kinds of restrictions
simultaneously by bounding, on the one hand, the atoms which are allowed to
occur in the rule heads of the context and, on the other hand, the atoms which
are allowed to occur in the rule bodies of the context. We introduce a general
semantical characterization which includes known ones as SE-models (for strong
equivalence) or UE-models (for uniform equivalence) as special cases.
Moreover,we provide complexity bounds for the problem in question and sketch a
possible implementation method.
To appear in Theory and Practice of Logic Programming (TPLP)
Constrained Query Answering
Traditional answering methods evaluate queries only against positive
and definite knowledge expressed by means of facts and deduction rules. They do
not make use of negative, disjunctive or existential information. Negative or indefinite
knowledge is however often available in knowledge base systems, either as
design requirements, or as observed properties. Such knowledge can serve to rule out
unproductive subexpressions during query answering. In this article, we propose an
approach for constraining any conventional query answering procedure with general,
possibly negative or indefinite formulas, so as to discard impossible cases and to
avoid redundant evaluations. This approach does not impose additional conditions
on the positive and definite knowledge, nor does it assume any particular semantics
for negation. It adopts that of the conventional query answering procedure it
constrains. This is achieved by relying on meta-interpretation for specifying the
constraining process. The soundness, completeness, and termination of the underlying
query answering procedure are not compromised. Constrained query answering
can be applied for answering queries more efficiently as well as for generating more
informative, intensional answers
Operational Semantics of Resolution and Productivity in Horn Clause Logic
This paper presents a study of operational and type-theoretic properties of
different resolution strategies in Horn clause logic. We distinguish four
different kinds of resolution: resolution by unification (SLD-resolution),
resolution by term-matching, the recently introduced structural resolution, and
partial (or lazy) resolution. We express them all uniformly as abstract
reduction systems, which allows us to undertake a thorough comparative analysis
of their properties. To match this small-step semantics, we propose to take
Howard's System H as a type-theoretic semantic counterpart. Using System H, we
interpret Horn formulas as types, and a derivation for a given formula as the
proof term inhabiting the type given by the formula. We prove soundness of
these abstract reduction systems relative to System H, and we show completeness
of SLD-resolution and structural resolution relative to System H. We identify
conditions under which structural resolution is operationally equivalent to
SLD-resolution. We show correspondence between term-matching resolution for
Horn clause programs without existential variables and term rewriting.Comment: Journal Formal Aspect of Computing, 201
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