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Stable models and circumscription
 Artificial Intelligence
"... The concept of a stable model provided a declarative semantics for Prolog programs with negation as failure and became a starting point for the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programmin ..."
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The concept of a stable model provided a declarative semantics for Prolog programs with negation as failure and became a starting point for the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programming and, unlike the original definition, refers neither to grounding nor to fixpoints. It is based on a syntactic transformation similar to parallel circumscription. 1
A Default Approach to Semantics of Logic Programs with Constraint Atoms
"... Abstract. We define the semantics of logic programs with (abstract) constraint atoms in a way closely tied to default logic. Like default logic, formulas in rules are evaluated using the classical entailment relation, so a constraint atom can be represented by an equivalent propositional formula. Th ..."
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Cited by 6 (3 self)
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Abstract. We define the semantics of logic programs with (abstract) constraint atoms in a way closely tied to default logic. Like default logic, formulas in rules are evaluated using the classical entailment relation, so a constraint atom can be represented by an equivalent propositional formula. Therefore, answer sets are defined in a way closely related to default extensions. The semantics defined this way enjoys two properties generally considered desirable for answer set programming − minimality and derivability. The derivability property is very important because it guarantees free of selfsupporting loops in answer sets. We show that when restricted to basic logic programs, this semantics agrees with the conditionalsatisfaction based semantics. Furthermore, answer sets by the minimalmodel based semantics can be recast in our approach. Consequently, the default approach gives a unifying account of the major existing semantics for logic programs with constraint atoms. This also makes it possible to characterize, in terms of the minimality and derivability properties, the precise relationship between them and contrast with others. 1
FirstOrder Extension of the FLP Stable Model Semantics via Modified Circumscription
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... We provide reformulations and generalizations of both the semantics of logic programs by Faber, Leone and Pfeifer and its extension to arbitrary propositional formulas by Truszczyński. Unlike the previous definitions, our generalizations refer neither to grounding nor to fixpoints, and apply to firs ..."
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Cited by 6 (2 self)
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We provide reformulations and generalizations of both the semantics of logic programs by Faber, Leone and Pfeifer and its extension to arbitrary propositional formulas by Truszczyński. Unlike the previous definitions, our generalizations refer neither to grounding nor to fixpoints, and apply to firstorder formulas containing aggregate expressions. In the same spirit as the firstorder stable model semantics proposed by Ferraris, Lee and Lifschitz, the semantics proposed here are based on syntactic transformations that are similar to circumscription. The reformulations provide useful insights into the FLP semantics and its relationship to circumscription and the firstorder stable model semantics.
Possibilistic Answer Set Programming Revisited
"... Possibilistic answer set programming (PASP) extends answer set programming (ASP) by attaching to each rule a degree of certainty. While such an extension is important from an application point of view, existing semantics are not wellmotivated, and do not always yield intuitive results. To develop a ..."
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Possibilistic answer set programming (PASP) extends answer set programming (ASP) by attaching to each rule a degree of certainty. While such an extension is important from an application point of view, existing semantics are not wellmotivated, and do not always yield intuitive results. To develop a more suitable semantics, we first introduce a characterization of answer sets of classical ASP programs in terms of possibilistic logic where an ASP program specifies a set of constraints on possibility distributions. This characterization is then naturally generalized to define answer sets of PASP programs. We furthermore provide a syntactic counterpart, leading to a possibilistic generalization of the wellknown GelfondLifschitz reduct, and we show how our framework can readily be implemented using standard ASP solvers. 1
Combining Nonmonotonic Knowledge Bases with External Sources ⋆
"... Abstract. The developments in information technology during the last decade have been rapidly changing the possibilities for data and knowledge access. To respect this, several declarative knowledge representation formalisms have been extended with the capability to access data and knowledge sources ..."
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Cited by 4 (3 self)
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Abstract. The developments in information technology during the last decade have been rapidly changing the possibilities for data and knowledge access. To respect this, several declarative knowledge representation formalisms have been extended with the capability to access data and knowledge sources that are external to a knowledge base. This article reviews some of these formalisms that are centered around Answer Set Programming, viz. HEXprograms, modular logic programs, and multicontext systems, which were developed by the KBS group of the Vienna University of Technology in cooperation with external colleagues. These formalisms were designed with different principles and four different settings, and thus have different properties and features; however, as argued, they are not unrelated. Furthermore, they provide a basis for advanced knowledgebased information systems, which are targeted in ongoing research projects. 1
From Database Repair Programs to Consistent Query Answering in Classical Logic (extended abstract)
"... Abstract. Consistent answers to a query from an inconsistent database are answers that can be simultaneously retrieved from every possible repair; and repairs are consistent instances that minimally differ from the original instance. Database repairs can be specified as the stable models of a disjun ..."
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Abstract. Consistent answers to a query from an inconsistent database are answers that can be simultaneously retrieved from every possible repair; and repairs are consistent instances that minimally differ from the original instance. Database repairs can be specified as the stable models of a disjunctive logic program. In this paper we show how to use the repair programs to transform the problem of consistent query answering into a problem of reasoning wrt a concrete theory written in secondorder predicate logic. It also investigated how a firstorder theory can be obtained instead, by applying secondorder quantifier elimination techniques. 1
FLP Semantics without Circular Justifications for General Logic Programs
"... The FLP semantics presented by (Faber, Leone, and Pfeifer 2004) has been widely used to define answer sets, called FLP answer sets, for different types of logic programs such as logic programs with aggregates, description logic programs (dlprograms), Hex programs, and logic programs with firstorde ..."
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The FLP semantics presented by (Faber, Leone, and Pfeifer 2004) has been widely used to define answer sets, called FLP answer sets, for different types of logic programs such as logic programs with aggregates, description logic programs (dlprograms), Hex programs, and logic programs with firstorder formulas (general logic programs). However, it was recently observed that the FLP semantics may produce unintuitive answer sets with circular justifications caused by selfsupporting loops. In this paper, we address the circular justification problem for general logic programs by enhancing the FLP semantics with a level mapping formalism. In particular, we extend the GelfondLifschitz three step definition of the standard answer set semantics from normal logic programs to general logic programs and define for general logic programs the first FLP semantics that is free of circular justifications. We call this FLP semantics the welljustified FLP semantics. This method naturally extends to general logic programs with additional constraints like aggregates, thus providing a unifying framework for defining the welljustified FLP semantics for various types of logic programs. When this method is applied to normal logic programs with aggregates, the welljustified FLP semantics agrees with the conditional satisfaction based semantics defined by (Son, Pontelli, and Tu 2007); and when applied to dlprograms, the semantics agrees with the strongly wellsupported semantics defined by (Shen 2011).
Guarded resolution for Answer Set Programming
, 2009
"... We investigate a proof system based on a guarded resolution rule and show its adequacy for stable semantics of normal logic programs. As a consequence, we show that GelfondLifschitz operator can be viewed as a prooftheoretic concept. As an application, we find a propositional theory whose models a ..."
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We investigate a proof system based on a guarded resolution rule and show its adequacy for stable semantics of normal logic programs. As a consequence, we show that GelfondLifschitz operator can be viewed as a prooftheoretic concept. As an application, we find a propositional theory whose models are precisely stable models of programs. EP 1
WellSupported Semantics for Logic Programs with Generalized Rules
"... Abstract. Logic programming under the stable model semantics has been extended to arbitrary formulas. A question of interest is how to characterize the property of wellsupportedness, in the sense of Fages, which has been considered a cornerstone in answer set programming. In this paper, we address ..."
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Abstract. Logic programming under the stable model semantics has been extended to arbitrary formulas. A question of interest is how to characterize the property of wellsupportedness, in the sense of Fages, which has been considered a cornerstone in answer set programming. In this paper, we address this issue by considering general logic programs, which consist of disjunctive rules with arbitrary propositional formulas in rule bodies. We define the justified stable semantics for these programs, propose a general notion of wellsupportedness, and show the relationships between the two. We address the issue of computational complexity for various classes of general programs. Finally, we show that previously proposed wellsupported semantics for aggregate programs and description logic programs are rooted in the justified stable semantics of general programs. 1
Logics of Contingency
"... We introduce the logic of positive and negative contingency. Together with modal operators of necessity and impossibility they allow to dispense of negation. We study classes of Kripke models where the number of points is restricted, and show that the modalities reduce in the corresponding logics. ..."
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We introduce the logic of positive and negative contingency. Together with modal operators of necessity and impossibility they allow to dispense of negation. We study classes of Kripke models where the number of points is restricted, and show that the modalities reduce in the corresponding logics.