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49
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.
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
Towards a systematic account of different semantics for logic programs
 Journal of Logic and Computation
"... Abstract. In [14,15], a new methodology has been proposed which allows to derive uniform characterizations of different declarative semantics for logic programs with negation. One result from this work is that the wellfounded semantics can formally be understood as a stratified version of the Fitti ..."
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Cited by 8 (6 self)
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Abstract. In [14,15], a new methodology has been proposed which allows to derive uniform characterizations of different declarative semantics for logic programs with negation. One result from this work is that the wellfounded semantics can formally be understood as a stratified version of the Fitting (or KripkeKleene) semantics. The constructions leading to this result, however, show a certain asymmetry which is not readily understood. We will study this situation here with the result that we will obtain a coherent picture of relations between different semantics for normal logic programs. 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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Cited by 8 (3 self)
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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.
Bilattices, intuitionism and truthknowledge duality: Concepts and foundations
, 2006
"... We propose a family of intuitionistic bilattices with full truthknowledge duality (Dbilattices) for a logic programming. The first family of perfect Dbilattices is composed by Boolean algebras with even number of atoms: the simplest of them, based on intuitionistic truthfunctionally complete ext ..."
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Cited by 8 (0 self)
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We propose a family of intuitionistic bilattices with full truthknowledge duality (Dbilattices) for a logic programming. The first family of perfect Dbilattices is composed by Boolean algebras with even number of atoms: the simplest of them, based on intuitionistic truthfunctionally complete extension of Belnap’s 4valued bilattice, can be used in paraconsistent programming, that is, for knowledge bases with incomplete and inconsistent information. The other two families are useful for a probability theory where the uncertainty in the knowledge about a piece of information is in the form of belief types: as an interval (lower and upper boundary) probability or as a confidence level. Such programs can be parameterized by different kinds of probabilistic conjunctive/disjunctive strategies for their rules, based on intuitionistic implication. Such a framework offers a clear semantics for the satisfaction relation, and allows the extension of logic languages with intuitionistic implications also in the body of rules. From a theoretical point of view we introduce also a duality in higherorder bilatices, as in Temporal Probabilistic Logic, constructed as functional spaces over ordinary dual bilattices. Then we show the full truthknowledge duality for a fixpoint semantics of logic programs based on dual bilattices. Finally we develop also an autoreferential version of Stone’s Representation Theorem for the dual bilattices.
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.
Data integration using IDlogic
 In Proc. 16th Int. Conf. on Advanced Information Systems Engineering (CAiSE’04), LNCS
, 2004
"... Abstract. IDLogic is a knowledge representation language that extends firstorder logic with nonmonotone inductive definitions. This paper introduces an IDLogic based framework for database schema integration. It allows us to to uniformly represent and reason with independent source databases ..."
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Abstract. IDLogic is a knowledge representation language that extends firstorder logic with nonmonotone inductive definitions. This paper introduces an IDLogic based framework for database schema integration. It allows us to to uniformly represent and reason with independent source databases that contain information about a common domain, but may have different schemas. The IDLogic theories that are obtained are called mediatorbased systems. We show that these theories properly capture the common methods for data integration (i.e., globalas view and localasview with either exact or partial definitions), and apply on them a robust abductive inference technique for query answering. 1
An algebraic account of modularity in IDlogic
 In Proc. LPNMR’05
, 2005
"... Abstract. IDlogic uses ideas from the field of logic programming to extend second order logic with nonmonotone inductive defintions. In this work, we reformulate the semantics of this logic in terms of approximation theory, an algebraic theory which generalizes the semantics of several nonmonoton ..."
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Cited by 5 (1 self)
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Abstract. IDlogic uses ideas from the field of logic programming to extend second order logic with nonmonotone inductive defintions. In this work, we reformulate the semantics of this logic in terms of approximation theory, an algebraic theory which generalizes the semantics of several nonmonotonic reasoning formalisms. This allows us to apply certain abstract modularity theorems, developed within the framework of approximation theory, to IDlogic. As such, we are able to offer elegant and simple proofs of generalizations of known theorems, as well as some new results. 1
Building a knowledge base system for an integration of logic programming and classical logic
 In ICLP. 71–76
"... Abstract. This paper presents a Knowledge Base project for FO(ID), an extension of classical logic with inductive definitions. This logic is a natural integration of classical logic and logic programming based on the view of a logic program as a definition. We discuss the relationship between induc ..."
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Abstract. This paper presents a Knowledge Base project for FO(ID), an extension of classical logic with inductive definitions. This logic is a natural integration of classical logic and logic programming based on the view of a logic program as a definition. We discuss the relationship between inductive definitions and common sense reasoning and the strong similarities and striking differences with ASP and Abductive LP. We report on inference systems that combine stateoftheart techniques of SAT and ASP. Experiments show that FO(ID) model expansion systems are competitive with the best ASPsolvers. 1