Results 1 
4 of
4
Extending Classical Logic with Inductive Definitions
, 2000
"... The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of nonmonotonic reasoning, logic programming and deductiv ..."
Abstract

Cited by 58 (38 self)
 Add to MetaCart
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of nonmonotonic reasoning, logic programming and deductive databases, and to show its application for knowledge representation by giving a typology of definitional knowledge.
The Wellfounded Semantics Is the Principle of Inductive Definition
 Logics in Arti Intelligence
, 1998
"... . Existing formalisations of (transfinite) inductive definitions in constructive mathematics are reviewed and strong correspondences with LP under least model and perfect model semantics become apparent. I point to fundamental restrictions of these existing formalisations and argue that the wellfou ..."
Abstract

Cited by 43 (26 self)
 Add to MetaCart
. Existing formalisations of (transfinite) inductive definitions in constructive mathematics are reviewed and strong correspondences with LP under least model and perfect model semantics become apparent. I point to fundamental restrictions of these existing formalisations and argue that the wellfounded semantics (wfs) overcomes these problems and hence, provides a superior formalisation of the principle of inductive definition. The contribution of this study for LP is that it (re )introduces the knowledge theoretic interpretation of LP as a logic for representing definitional knowledge. I point to fundamental differences between this knowledge theoretic interpretation of LP and the more commonly known interpretations of LP as default theories or autoepistemic theories. The relevance is that differences in knowledge theoretic interpretation have strong impact on knowledge representation methodology and on extensions of the LP formalism, for example for representing uncertainty. Keywo...
Executing Suspended Logic Programs
 FUNDAMENTA INFORMATICAE
, 1998
"... We present an extension of Logic Programming (LP) which, in addition to ordinary LP clauses, also includes integrity constraints, explicit representation of disjunction in the bodies of clauses and in goals, and suspension of atoms as in concurrent logic languages. The resulting framework aims to ..."
Abstract

Cited by 24 (11 self)
 Add to MetaCart
We present an extension of Logic Programming (LP) which, in addition to ordinary LP clauses, also includes integrity constraints, explicit representation of disjunction in the bodies of clauses and in goals, and suspension of atoms as in concurrent logic languages. The resulting framework aims to unify Constraint Logic Programming (CLP), Abductive Logic Programming (ALP) and Semantic Query Optimisation (SQO) in deductive databases. We present a proof procedure for the new framework, simplifying and generalising previously proposed proof procedures for ALP. We discuss applications of the framework, formulating traditional problems from LP, ALP, CLP and SQO.
Logic Programs as Definitions: a framework for and an evaluation of its semantics
"... We present a formal theory on the semantics of logic programs and abductive logic programs with first order integrity constraints. The theory provides an elegant, uniform formalisation for the three most widely accepted families of semantics: completion semantics, stable semantics and wellfounded se ..."
Abstract
 Add to MetaCart
We present a formal theory on the semantics of logic programs and abductive logic programs with first order integrity constraints. The theory provides an elegant, uniform formalisation for the three most widely accepted families of semantics: completion semantics, stable semantics and wellfounded semantics. The theory is based on the notion of a justification, which is a mathematical object describing, given an interpretation, how the truth value of a literal can be justified on the basis of the program. We identify the three different notions of justifications underlying the three types of semantics. In addition, we defend an alternative declarative reading of logic programming, different from the current predominant view of logic programming as a form of defeasible logic. Logic programs are interpreted as sets of definitions of predicates. The framework is suited to evaluate the extent to which this intuition is supported by the three classes of semantics. 1 Introduction. At this mo...