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51
An Inductive Definition Approach to Ramifications
 IN ELECTRONIC TRANSACTIONS ON ARTIFICIAL INTELLIGENCE
, 1998
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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.
Experiments for integration CLP and abduction
 Workshop on Constraints
, 1999
"... 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 specifications. The IDlogic logic is a ..."
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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 specifications. The IDlogic logic 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 some preliminary computational experiments with an integration of the abductive reasoner SLDNFA and CLPsystems.
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.
Ultimate Approximations in Nonmonotonic Knowledge Representation Systems
 IN PRINCIPLES OF KNOWLEDGE REPRESENTATION AND REASONING, PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE (KR2002
, 2002
"... We study fixpoints of operators on lattices. To this end ..."
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We study fixpoints of operators on lattices. To this end
Predicate logic as a modelling language: The IDP system
, 2014
"... per Predicate Logic as a Programming Language was a breakthrough for the use of logic in computer science. The more recent tremendous progress in automated reasoning technologies, particularly in SAT solving and Constraint Programming, has paved the way for the use of logic as a modelling language. ..."
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per Predicate Logic as a Programming Language was a breakthrough for the use of logic in computer science. The more recent tremendous progress in automated reasoning technologies, particularly in SAT solving and Constraint Programming, has paved the way for the use of logic as a modelling language. This paper describes the realisation of such a modelling language as the IDP knowledgebase system (KBS). In contrast to declarative programming, the user only specifies her knowledge about a problem and has not to pay attention to control issues. In the IDP system, declarative modelling is done in the language FO(·)IDP which combines inductive definitions (similar to sets of Prolog rules) with firstorder logic, types and aggregates, allowing for concise specifications. The paper presents the language, motivates the design choices and gives an overview of the system architecture and the implementation techniques. It also gives an overview of different inference tasks supported by the system such as query evaluation, model expansion and theorem proving, and explains in detail how combining various functionalities results in a stateoftheart model expansion engine. Finally, it explains how a tight integration with a procedural language (Lua) allows users to treat logical components as firstclass citizens and to solve complex problems in a workflow of (multiinference) interactions. 1
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
What’s in a model? Epistemological analysis of logic programming
 Proceedings of the 9th International Conference on PrinICLP 2012 A Tarskian Informal Semantics for ASP ciples of Knowledge Representation and Reasoning
, 2004
"... It is commonly believed that the meaning of a formal declarative knowledge representation language is determined by its formal semantics. This is not quite so. This paper shows an epistemological ambiguity that arises in the context of logic programming. Several different logic programming formali ..."
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It is commonly believed that the meaning of a formal declarative knowledge representation language is determined by its formal semantics. This is not quite so. This paper shows an epistemological ambiguity that arises in the context of logic programming. Several different logic programming formalisms and semantics have been proposed. Hence, logic programming can be seen as an overlapping family of formal logics, each induced by a pair of a formal syntax and a formal semantics. We would expect that (a) each such pair has a unique declarative reading and (b) for a program in the intersection of several formal LP logics with the same formal semantics in each of them, its declarative reading is the same in each of them. I show in this paper that neither (a) nor (b) holds. The paper investigates the causes and the consequences of this phenomenon and points out some directions to overcome the ambiguity.
Satisfiability checking for PC(ID)
, 2005
"... 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 integrati ..."
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Cited by 7 (2 self)
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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.
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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Cited by 6 (5 self)
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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.