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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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Cited by 55 (37 self)
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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
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
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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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
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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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
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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Cited by 2 (0 self)
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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).
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
Modularity of Plog programs
"... Abstract. We propose an approach for modularizing Plog programs and corresponding compositional semantics based on conditional probability measures. We do so by resorting to Oikarinen and Janhunen’s definition of a logic program module and extending it to Plog by introducing the notions of input r ..."
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Abstract. We propose an approach for modularizing Plog programs and corresponding compositional semantics based on conditional probability measures. We do so by resorting to Oikarinen and Janhunen’s definition of a logic program module and extending it to Plog by introducing the notions of input random attributes and output literals. For answering to Plog queries our method does not imply calculating all the stable models (possible worlds) of a given program, and previous calculations can be reused. Our proposal also handles probabilistic evidence by conditioning (observations).
Extending Answer Set Programming Proefschrift ingediend met het oog op het behalen van de graad
"... I would like to express my sincere gratitude to a number of people who have made the completion of this thesis possible. I would like to thank my promotor Dirk Vermeir for introducing me to the field of answer set programming in the first place and for helping me in almost every aspect of writing a ..."
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I would like to express my sincere gratitude to a number of people who have made the completion of this thesis possible. I would like to thank my promotor Dirk Vermeir for introducing me to the field of answer set programming in the first place and for helping me in almost every aspect of writing a thesis. He has helped me in pinning down a thesis subject, has pointed me to some valuable resources regarding answer set programming and has been a trustworthy sounding board for my ideas. I would also like to thank Jeroen Janssen and Steven Schockaert. We met at just the right time and they helped to focus the content of my thesis and brought me back on track by asking just the right questions at a time when I was lost. Special thanks go out to Jeroen Janssen for proofreading my thesis in such a short timeframe. The quality of this thesis would certainly not be on par with the current quality if it was not for his priceless input. I would like to thank my parents and brother for always being there and loving me unconditionally. Special thanks go out to my parents for their
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.