40,338 research outputs found
Tabling with Sound Answer Subsumption
Tabling is a powerful resolution mechanism for logic programs that captures
their least fixed point semantics more faithfully than plain Prolog. In many
tabling applications, we are not interested in the set of all answers to a
goal, but only require an aggregation of those answers. Several works have
studied efficient techniques, such as lattice-based answer subsumption and
mode-directed tabling, to do so for various forms of aggregation.
While much attention has been paid to expressivity and efficient
implementation of the different approaches, soundness has not been considered.
This paper shows that the different implementations indeed fail to produce
least fixed points for some programs. As a remedy, we provide a formal
framework that generalises the existing approaches and we establish a soundness
criterion that explains for which programs the approach is sound.
This article is under consideration for acceptance in TPLP.Comment: Paper presented at the 32nd International Conference on Logic
Programming (ICLP 2016), New York City, USA, 16-21 October 2016, 15 pages,
LaTeX, 0 PDF figure
Epistemic Foundation of Stable Model Semantics
Stable model semantics has become a very popular approach for the management
of negation in logic programming. This approach relies mainly on the closed
world assumption to complete the available knowledge and its formulation has
its basis in the so-called Gelfond-Lifschitz transformation.
The primary goal of this work is to present an alternative and
epistemic-based characterization of stable model semantics, to the
Gelfond-Lifschitz transformation. In particular, we show that stable model
semantics can be defined entirely as an extension of the Kripke-Kleene
semantics. Indeed, we show that the closed world assumption can be seen as an
additional source of `falsehood' to be added cumulatively to the Kripke-Kleene
semantics. Our approach is purely algebraic and can abstract from the
particular formalism of choice as it is based on monotone operators (under the
knowledge order) over bilattices only.Comment: 41 pages. To appear in Theory and Practice of Logic Programming
(TPLP
Information completeness in Nelson algebras of rough sets induced by quasiorders
In this paper, we give an algebraic completeness theorem for constructive
logic with strong negation in terms of finite rough set-based Nelson algebras
determined by quasiorders. We show how for a quasiorder , its rough
set-based Nelson algebra can be obtained by applying the well-known
construction by Sendlewski. We prove that if the set of all -closed
elements, which may be viewed as the set of completely defined objects, is
cofinal, then the rough set-based Nelson algebra determined by a quasiorder
forms an effective lattice, that is, an algebraic model of the logic ,
which is characterised by a modal operator grasping the notion of "to be
classically valid". We present a necessary and sufficient condition under which
a Nelson algebra is isomorphic to a rough set-based effective lattice
determined by a quasiorder.Comment: 15 page
An analysis of the equational properties of the well-founded fixed point
Well-founded fixed points have been used in several areas of knowledge
representation and reasoning and to give semantics to logic programs involving
negation. They are an important ingredient of approximation fixed point theory.
We study the logical properties of the (parametric) well-founded fixed point
operation. We show that the operation satisfies several, but not all of the
equational properties of fixed point operations described by the axioms of
iteration theories
Introducing Dynamic Behavior in Amalgamated Knowledge Bases
The problem of integrating knowledge from multiple and heterogeneous sources
is a fundamental issue in current information systems. In order to cope with
this problem, the concept of mediator has been introduced as a software
component providing intermediate services, linking data resources and
application programs, and making transparent the heterogeneity of the
underlying systems. In designing a mediator architecture, we believe that an
important aspect is the definition of a formal framework by which one is able
to model integration according to a declarative style. To this purpose, the use
of a logical approach seems very promising. Another important aspect is the
ability to model both static integration aspects, concerning query execution,
and dynamic ones, concerning data updates and their propagation among the
various data sources. Unfortunately, as far as we know, no formal proposals for
logically modeling mediator architectures both from a static and dynamic point
of view have already been developed. In this paper, we extend the framework for
amalgamated knowledge bases, presented by Subrahmanian, to deal with dynamic
aspects. The language we propose is based on the Active U-Datalog language, and
extends it with annotated logic and amalgamation concepts. We model the sources
of information and the mediator (also called supervisor) as Active U-Datalog
deductive databases, thus modeling queries, transactions, and active rules,
interpreted according to the PARK semantics. By using active rules, the system
can efficiently perform update propagation among different databases. The
result is a logical environment, integrating active and deductive rules, to
perform queries and update propagation in an heterogeneous mediated framework.Comment: Other Keywords: Deductive databases; Heterogeneous databases; Active
rules; Update
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