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Paraconsistent Declarative Semantics for Extended Logic Programs
 Annals of Mathematics and Artificial Intelligence
, 2002
"... We introduce a fixpoint semantics for logic programs with two kinds of negation:... ..."
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We introduce a fixpoint semantics for logic programs with two kinds of negation:...
What's in a Model? Epistemological analysis of Logic Programming
 CeurWS
, 2003
"... The paper is an epistemological analysis of logic programming and shows an epistemological ambiguity. Many different logic programming formalisms and semantics have been proposed. Hence, logic programming can be seen as a family of formal logics, each induced by a pair of a syntax and a semantics ..."
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Cited by 8 (3 self)
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The paper is an epistemological analysis of logic programming and shows an epistemological ambiguity. Many different logic programming formalisms and semantics have been proposed. Hence, logic programming can be seen as a family of formal logics, each induced by a pair of a syntax and a semantics, and each having a different declarative reading. However, we may expect that (a) if a program belongs to different logics of this family and has the same formal semantics in these logics, then the declarative meaning attributed to this program in the different logics is equivalent, and (b) that one and the same logic in this family has not been associated with distinct declarative readings.
Satisfiability checking for PC(ID
 In LPAR
, 2005
"... Abstract. The logic FO(ID) extends classical first order logic with inductive definitions. This paper studies the satisifiability problem for PC(ID), its propositional fragment. We develop a framework for model generation in this logic, present an algorithm and prove its correctness. As FO(ID) is an ..."
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Abstract. The logic FO(ID) extends classical first order logic with inductive definitions. This paper studies the satisifiability problem for PC(ID), its propositional fragment. We develop a framework for model generation in this logic, present an algorithm and prove its correctness. As FO(ID) is an integration of classical logic and logic programming, our algorithm integrates techniques from SAT and ASP. We report on a prototype system, called MidL, experimentally validating our approach. 1
Logic Programming for Knowledge Representation
, 2007
"... This note provides background information and references to the tutorial on recent research developments in logic programming inspired by need of knowledge representation. ..."
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This note provides background information and references to the tutorial on recent research developments in logic programming inspired by need of knowledge representation.
An epistemic foundation of stable model semantics
, 2003
"... The stable model semantics has become a dominating approach for the management of negation in logic programming. It relies mainly on the closed world assumption to complete the available knowledge and its formulation has its founding root in the socalled GelfondLifschitz transform. The primary goa ..."
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The stable model semantics has become a dominating approach for the management of negation in logic programming. It relies mainly on the closed world assumption to complete the available knowledge and its formulation has its founding root in the socalled GelfondLifschitz transform. The primary goal of this work is to present an alternative and epistemic based characterization of the stable model semantics, to the GelfondLifschitz transform. In particular, we show that the stable model semantics can be defined entirely as an extension of the KripkeKleene semantics and, thus, (i) does rely on the classical management of negation; and (ii) does not require any program transformation. Indeed, we show that the closed world assumption can be seen as an additional source for ‘falsehood ’ to be added cumulatively to the KripkeKleene 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.
Connecting firstorder ASP and the logic FO(ID) through reducts
 In: Correct Reasoning: Essays on LogicBased AI in Honor of Vladimir Lifschitz
, 2012
"... on his 65th birthday! Abstract. Recently, an answerset programming (ASP) formalism of logic programing with the answerset semantics has been extended to the full firstorder setting. Earlier an extension of firstorder logic with inductive definitions, the logic FO(ID), was proposed as a knowledge ..."
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on his 65th birthday! Abstract. Recently, an answerset programming (ASP) formalism of logic programing with the answerset semantics has been extended to the full firstorder setting. Earlier an extension of firstorder logic with inductive definitions, the logic FO(ID), was proposed as a knowledge representation formalism and developed as an alternative ASP language. We present characterizations of these formalisms in terms of concepts of infinitary propositional logic. We use them to find a direct connection between the firstorder ASP and the logic FO(ID) under some restrictions on the form of theories (programs) considered. 1
Prescriptive Type Inference as an Application of Abduction: Extended Abstract
, 1999
"... This paper compares the tasks of type checking and type inference in the context of a simple manysorted prescriptive type system. Type inference is an extension of type checking in the context of incomplete type declarations; while checking the welltypedness of some expressions, type inference als ..."
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This paper compares the tasks of type checking and type inference in the context of a simple manysorted prescriptive type system. Type inference is an extension of type checking in the context of incomplete type declarations; while checking the welltypedness of some expressions, type inference also infers type declarations for undeclared symbols. The basis of our approach is a declarative representation of the concept of a welltyped expression by a formal denition in a logic theory. We show that type checking can be implemented as a deductive task with respect to this logical theory augmented with an exhaustive enumeration of type declarations. We show that type inference can be implemented as an abductive task with respect to the same logical theory augmented with a partial enumeration of type declarations and some axioms expressing general properties of the type system. 1 Introduction This paper studies two tasks in the context of a simple manysorted prescriptive type system...
Problem solving in IDlogic with aggregates: some experiments
 8TH INT. WORKSHOP ON NONMONOTONIC REASONING (NMR2000), SESSION ON ABDUCTION
, 2000
"... The goal of the LP+ project at the K.U.Leuven is to design an expressive logic, suitable for declarative knowledge representation, and to develop intelligent systems based on Logic Programming technology for solving computational problems using the declarative specications. The IDlogic is an integr ..."
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The goal of the LP+ project at the K.U.Leuven is to design an expressive logic, suitable for declarative knowledge representation, and to develop intelligent systems based on Logic Programming technology for solving computational problems using the declarative specications. The IDlogic is an integration of typed classical logic and a definition logic. Different abductive solvers for this language are being developed. This paper is a report of the integration of high order aggregates into IDlogic and the consequences on the solver SLDNFA.
A Tarskian Informal Semantics for Answer Set Programming ∗
"... In their seminal papers on stable model semantics, Gelfond and Lifschitz introduced ASP by casting programs as epistemic theories, in which rules represent statements about the knowledge of a rational agent. To the best of our knowledge, theirs is still the only published systematic account of the i ..."
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In their seminal papers on stable model semantics, Gelfond and Lifschitz introduced ASP by casting programs as epistemic theories, in which rules represent statements about the knowledge of a rational agent. To the best of our knowledge, theirs is still the only published systematic account of the intuitive meaning of rules and programs under the stable semantics. In current ASP practice, however, we find numerous applications in which rational agents no longer seem to play any role. Therefore, we propose here an alternative explanation of the intuitive meaning of ASP programs, in which they are not viewed as statements about an agent’s beliefs, but as objective statements about the world. We argue that this view is more natural for a large part of current ASP practice, in particular the socalled GenerateDefineTest programs.
On the Epistemological foundations of Logic Programming and its Extensions
, 2001
"... One of the major roles of logic in computer science and A.I. is for knowledge representation and specication. In the context of knowledge representation, formal logic is widely praised as the tool par excellence for expressing information in a precise way and for correct and precise communication of ..."
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One of the major roles of logic in computer science and A.I. is for knowledge representation and specication. In the context of knowledge representation, formal logic is widely praised as the tool par excellence for expressing information in a precise way and for correct and precise communication of information between dierent experts. In the scenario of communicating experts, the experts express their knowledge about some external problem domain in logic specications which subsequently are communicated to other experts. In the computational logic approach to AI, computers participate in this and assist the human experts by solving computational problems using the logic specications. The use of formal logic helps to avoid the ambiguities and lacunas that appear frequently in natural language specications and, in a absence of computer systems that understand natural language, is the most promising way of transferring knowledge to a computer system. Obviously, when dierent human ex...