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Reconciling description logics and rules
, 2010
"... Description logics (DLs) and rules are formalisms that emphasize different aspects of knowledge representation: whereas DLs are focused on specifying and reasoning about conceptual knowledge, rules are focused on nonmonotonic inference. Many applications, however, require features of both DLs and ru ..."
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Cited by 81 (0 self)
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Description logics (DLs) and rules are formalisms that emphasize different aspects of knowledge representation: whereas DLs are focused on specifying and reasoning about conceptual knowledge, rules are focused on nonmonotonic inference. Many applications, however, require features of both DLs and rules. Developing a formalism that integrates DLs and rules would be a natural outcome of a large body of research in knowledge representation and reasoning of the last two decades; however, achieving this goal is very challenging and the approaches proposed thus far have not fully reached it. In this paper, we present a hybrid formalism of MKNF + knowledge bases, which integrates DLs and rules in a coherent semantic framework. Achieving seamless integration is nontrivial, since DLs use an openworld assumption, while the rules are based on a closedworld assumption. We overcome this discrepancy by basing the semantics of our formalism on the logic of minimal knowledge and negation as failure (MKNF) by Lifschitz. We present several algorithms for reasoning with MKNF + knowledge bases, each suitable to different kinds of rules, and establish tight complexity bounds.
A new perspective on stable models
 In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI
, 2007
"... The definition of a stable model has provided a declarative semantics for Prolog programs with negation as failure and has led to 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 (includi ..."
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Cited by 77 (32 self)
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The definition of a stable model has provided a declarative semantics for Prolog programs with negation as failure and has led to 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 (including disjunctive rules, choice rules and conditional literals) and, unlike the original definition, refers neither to grounding nor to fixpoints. Rather, it is based on a syntactic transformation, which turns a logic program into a formula of secondorder logic that is similar to the formula familiar from the definition of circumscription. 1
Stable Models and Circumscription
, 2007
"... The definition of a stable model has provided a declarative semantics for Prolog programs with negation as failure and has led to 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 (includ ..."
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Cited by 71 (37 self)
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The definition of a stable model has provided a declarative semantics for Prolog programs with negation as failure and has led to 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 (including disjunctive rules, choice rules and conditional literals) and, unlike the original definition, refers neither to grounding nor to fixpoints. Rather, it is based on a syntactic transformation, which turns a logic program into a formula of secondorder logic that is similar to the formula familiar from John McCarthy’s definition of circumscription.
Reformulating the Situation Calculus and the Event Calculus
 In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI),
, 2008
"... Abstract Circumscription and logic programs under the stable model semantics are two wellknown nonmonotonic formalisms. The former has served as a basis of classical logic based action formalisms, such as the situation calculus, the event calculus and temporal action logics; the latter has served a ..."
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Cited by 9 (4 self)
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Abstract Circumscription and logic programs under the stable model semantics are two wellknown nonmonotonic formalisms. The former has served as a basis of classical logic based action formalisms, such as the situation calculus, the event calculus and temporal action logics; the latter has served as a basis of a family of action languages, such as language A and several of its descendants. Based on the discovery that circumscription and the stable model semantics coincide on a class of canonical formulas, we reformulate the situation calculus and the event calculus in the general theory of stable models. We also present a translation that turns the reformulations further into answer set programs, so that efficient answer set solvers can be applied to compute the situation calculus and the event calculus.
D.: A logical semantics for description logic programs
 JELIA 2010. LNCS
, 2010
"... Abstract. We present a new semantics for Description Logic programs [1] (dlprograms) that combine reasoning about ontologies in description logics with nonmonotonic rules interpreted under answer set semantics. Our semantics is equivalent to that of [1], but is more logical in style, being based o ..."
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Cited by 6 (1 self)
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Abstract. We present a new semantics for Description Logic programs [1] (dlprograms) that combine reasoning about ontologies in description logics with nonmonotonic rules interpreted under answer set semantics. Our semantics is equivalent to that of [1], but is more logical in style, being based on the logic QHT of quantified hereandthere that provides a foundation for ordinary logic programs under answer set semantics and removes the need for program reducts. Here we extend the concept of QHTmodel to encompass dlprograms. As an application we characterise some logical relations between dlprograms, by mating the idea ofQHTequivalence with the concept of query inseparability taken from description logics. 1
Characterising equilibrium logic and nested logic programs: Reductions and complexity
, 2009
"... Equilibrium logic is an approach to nonmonotonic reasoning that extends the stablemodel and answerset semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations are permitted in heads and bodies of rules, as special kind ..."
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Cited by 6 (2 self)
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Equilibrium logic is an approach to nonmonotonic reasoning that extends the stablemodel and answerset semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations are permitted in heads and bodies of rules, as special kinds of theories. In this paper, we present polynomial reductions of the main reasoning tasks associated with equilibrium logic and nested logic programs into quantified propositional logic, an extension of classical propositional logic where quantifications over atomic formulas are permitted. Thus, quantified propositional logic is a fragment of secondorder logic, and its formulas are usually referred to as quantified Boolean formulas (QBFs). We provide reductions not only for decision problems, but also for the central semantical concepts of equilibrium logic and nested logic programs. In particular, our encodings map a given decision problem into some QBF such that the latter is valid precisely in case the former holds. The basic tasks we deal with here are the consistency problem, brave reasoning, and skeptical reasoning. Additionally, we also provide encodings for testing equivalence of theories or programs under different notions
178 Stable Model Semantics and FirstOrder Loop Formulas
 In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI
, 2005
"... Lin and Zhao’s theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the firstorder case. We investigate the precise relationship betwe ..."
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Cited by 4 (1 self)
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Lin and Zhao’s theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the firstorder case. We investigate the precise relationship between the firstorder stable model semantics and firstorder loop formulas, and study conditions under which the former can be represented by the latter. In order to facilitate the comparison, we extend the definition of a firstorder loop formula which was limited to a nondisjunctive program, to a disjunctive program and to an arbitrary firstorder theory. Based on the studied relationship we extend the syntax of a logic program with explicit quantifiers, which allows us to do reasoning involving nonHerbrand stable models using firstorder reasoners. Such programs can be viewed as a special class of firstorder theories under the stable model semantics, which yields more succinct loop formulas than the general language due to their restricted syntax. 1.
Tableau Calculi for Logic Programs under Answer Set Semantics
"... We introduce formal proof systems based on tableau methods for analyzing computations in Answer Set Programming (ASP). Our approach furnishes finegrained instruments for characterizing operations as well as strategies of ASP solvers. The granularity is detailed enough to capture a variety of propag ..."
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Cited by 3 (1 self)
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We introduce formal proof systems based on tableau methods for analyzing computations in Answer Set Programming (ASP). Our approach furnishes finegrained instruments for characterizing operations as well as strategies of ASP solvers. The granularity is detailed enough to capture a variety of propagation and choice methods of algorithms used for ASP solving, also incorporating SATbased and conflictdriven learning approaches to some extent. This provides us with a uniform setting for identifying and comparing fundamental properties of ASP solving approaches. In particular, we investigate their proof complexities and show that the runtimes of bestcase computations can vary exponentially between different existing ASP solvers. Apart from providing a framework for comparing ASP solving approaches, our characterizations also contribute to their understanding by pinning down the constitutive atomic operations. Furthermore, our framework is flexible enough to integrate new inference patterns, and so to study their relation to existing ones. To this end, we generalize our approach and provide an extensible basis aiming at a modular incorporation of additional language constructs. This is exemplified by augmenting our basic tableau methods with cardinality constraints and disjunctions.
FQHT: The Logic of Stable Models for Logic Programs with Intensional Functions
 PROCEEDINGS OF THE TWENTYTHIRD INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2013
"... We study a logical system FQHT that is appropriate for reasoning about nonmonotonic theories with intensional functions as treated in the approach of [Bartholomew and Lee, 2012]. We provide a logical semantics, a Gentzen style proof theory and establish completeness results. The adequacy of the appr ..."
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Cited by 2 (0 self)
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We study a logical system FQHT that is appropriate for reasoning about nonmonotonic theories with intensional functions as treated in the approach of [Bartholomew and Lee, 2012]. We provide a logical semantics, a Gentzen style proof theory and establish completeness results. The adequacy of the approach is demonstrated by showing that it captures the Bartholemew/Lee semantics and satisfies a strong equivalence property.
Translating FirstOrder Theories into Logic Programs
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... This paper focuses on computing firstorder theories under either stable model semantics or circumscription. A reduction from firstorder theories to logic programs under stable model semantics over finite structures is proposed, and an embedding of circumscription into stable model semantics is als ..."
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This paper focuses on computing firstorder theories under either stable model semantics or circumscription. A reduction from firstorder theories to logic programs under stable model semantics over finite structures is proposed, and an embedding of circumscription into stable model semantics is also given. Having such reduction and embedding, reasoning problems represented by firstorder theories under these two semantics can then be handled by using existing answer set solvers. The effectiveness of this approach in computing hard problems beyond NP is demonstrated by some experiments.