21,715 research outputs found
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
An algebraic generalization of Kripke structures
The Kripke semantics of classical propositional normal modal logic is made
algebraic via an embedding of Kripke structures into the larger class of
pointed stably supported quantales. This algebraic semantics subsumes the
traditional algebraic semantics based on lattices with unary operators, and it
suggests natural interpretations of modal logic, of possible interest in the
applications, in structures that arise in geometry and analysis, such as
foliated manifolds and operator algebras, via topological groupoids and inverse
semigroups. We study completeness properties of the quantale based semantics
for the systems K, T, K4, S4, and S5, in particular obtaining an axiomatization
for S5 which does not use negation or the modal necessity operator. As
additional examples we describe intuitionistic propositional modal logic, the
logic of programs PDL, and the ramified temporal logic CTL.Comment: 39 page
Disjunctive Logic Programs with Inheritance
The paper proposes a new knowledge representation language, called DLP<,
which extends disjunctive logic programming (with strong negation) by
inheritance. The addition of inheritance enhances the knowledge modeling
features of the language providing a natural representation of default
reasoning with exceptions.
A declarative model-theoretic semantics of DLP< is provided, which is shown
to generalize the Answer Set Semantics of disjunctive logic programs.
The knowledge modeling features of the language are illustrated by encoding
classical nonmonotonic problems in DLP<.
The complexity of DLP< is analyzed, proving that inheritance does not cause
any computational overhead, as reasoning in DLP< has exactly the same
complexity as reasoning in disjunctive logic programming. This is confirmed by
the existence of an efficient translation from DLP< to plain disjunctive logic
programming. Using this translation, an advanced KR system supporting the DLP<
language has been implemented on top of the DLV system and has subsequently
been integrated into DLV.Comment: 28 pages; will be published in Theory and Practice of Logic
Programmin
Proving Correctness and Completeness of Normal Programs - a Declarative Approach
We advocate a declarative approach to proving properties of logic programs.
Total correctness can be separated into correctness, completeness and clean
termination; the latter includes non-floundering. Only clean termination
depends on the operational semantics, in particular on the selection rule. We
show how to deal with correctness and completeness in a declarative way,
treating programs only from the logical point of view. Specifications used in
this approach are interpretations (or theories). We point out that
specifications for correctness may differ from those for completeness, as
usually there are answers which are neither considered erroneous nor required
to be computed.
We present proof methods for correctness and completeness for definite
programs and generalize them to normal programs. For normal programs we use the
3-valued completion semantics; this is a standard semantics corresponding to
negation as finite failure. The proof methods employ solely the classical
2-valued logic. We use a 2-valued characterization of the 3-valued completion
semantics which may be of separate interest. The presented methods are compared
with an approach based on operational semantics. We also employ the ideas of
this work to generalize a known method of proving termination of normal
programs.Comment: To appear in Theory and Practice of Logic Programming (TPLP). 44
page
Fixpoint semantics for logic programming a survey
AbstractThe variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies
Characterizing and Extending Answer Set Semantics using Possibility Theory
Answer Set Programming (ASP) is a popular framework for modeling
combinatorial problems. However, ASP cannot easily be used for reasoning about
uncertain information. Possibilistic ASP (PASP) is an extension of ASP that
combines possibilistic logic and ASP. In PASP a weight is associated with each
rule, where this weight is interpreted as the certainty with which the
conclusion can be established when the body is known to hold. As such, it
allows us to model and reason about uncertain information in an intuitive way.
In this paper we present new semantics for PASP, in which rules are interpreted
as constraints on possibility distributions. Special models of these
constraints are then identified as possibilistic answer sets. In addition,
since ASP is a special case of PASP in which all the rules are entirely
certain, we obtain a new characterization of ASP in terms of constraints on
possibility distributions. This allows us to uncover a new form of disjunction,
called weak disjunction, that has not been previously considered in the
literature. In addition to introducing and motivating the semantics of weak
disjunction, we also pinpoint its computational complexity. In particular,
while the complexity of most reasoning tasks coincides with standard
disjunctive ASP, we find that brave reasoning for programs with weak
disjunctions is easier.Comment: 39 pages and 16 pages appendix with proofs. This article has been
accepted for publication in Theory and Practice of Logic Programming,
Copyright Cambridge University Pres
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