9,114 research outputs found
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
Computing only minimal answers in disjunctive deductive databases
A method is presented for computing minimal answers in disjunctive deductive
databases under the disjunctive stable model semantics. Such answers are
constructed by repeatedly extending partial answers. Our method is complete (in
that every minimal answer can be computed) and does not admit redundancy (in
the sense that every partial answer generated can be extended to a minimal
answer), whence no non-minimal answer is generated. For stratified databases,
the method does not (necessarily) require the computation of models of the
database in their entirety. Compilation is proposed as a tool by which problems
relating to computational efficiency and the non-existence of disjunctive
stable models can be overcome. The extension of our method to other semantics
is also considered.Comment: 48 page
Logic Programming Applications: What Are the Abstractions and Implementations?
This article presents an overview of applications of logic programming,
classifying them based on the abstractions and implementations of logic
languages that support the applications. The three key abstractions are join,
recursion, and constraint. Their essential implementations are for-loops, fixed
points, and backtracking, respectively. The corresponding kinds of applications
are database queries, inductive analysis, and combinatorial search,
respectively. We also discuss language extensions and programming paradigms,
summarize example application problems by application areas, and touch on
example systems that support variants of the abstractions with different
implementations
Semantics of logic programs with explicit negation
After a historical introduction, the bulk of the thesis concerns the study of a declarative semantics for logic programs. The main original contributions are: ² WFSX (Well–Founded Semantics with eXplicit negation), a new semantics for logic programs with explicit negation (i.e. extended logic programs), which compares favourably in its properties with other extant semantics. ² A generic characterization schema that facilitates comparisons among a diversity of semantics of extended logic programs, including WFSX. ² An autoepistemic and a default logic corresponding to WFSX, which solve existing problems of the classical approaches to autoepistemic and default logics, and clarify the meaning of explicit negation in logic programs. ² A framework for defining a spectrum of semantics of extended logic programs based on the abduction of negative hypotheses. This framework allows for the characterization of different levels of scepticism/credulity, consensuality, and argumentation. One of the semantics of abduction coincides with WFSX. ² O–semantics, a semantics that uniquely adds more CWA hypotheses to WFSX. The techniques used for doing so are applicable as well to the well–founded semantics of normal logic programs. ² By introducing explicit negation into logic programs contradiction may appear. I present two approaches for dealing with contradiction, and show their equivalence. One of the approaches consists in avoiding contradiction, and is based on restrictions in the adoption of abductive hypotheses. The other approach consists in removing contradiction, and is based in a transformation of contradictory programs into noncontradictory ones, guided by the reasons for contradiction
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
Answer Set Programming Modulo `Space-Time'
We present ASP Modulo `Space-Time', a declarative representational and
computational framework to perform commonsense reasoning about regions with
both spatial and temporal components. Supported are capabilities for mixed
qualitative-quantitative reasoning, consistency checking, and inferring
compositions of space-time relations; these capabilities combine and synergise
for applications in a range of AI application areas where the processing and
interpretation of spatio-temporal data is crucial. The framework and resulting
system is the only general KR-based method for declaratively reasoning about
the dynamics of `space-time' regions as first-class objects. We present an
empirical evaluation (with scalability and robustness results), and include
diverse application examples involving interpretation and control tasks
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