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77
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.
Answer Sets
, 2007
"... This chapter is an introduction to Answer Set Prolog a language for knowledge representation and reasoning based on the answer set/stable model semantics of logic programs [44, 45]. The language has roots in declarative programing [52, 65], the syntax and semantics of standard Prolog [24, 23], disj ..."
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Cited by 62 (5 self)
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This chapter is an introduction to Answer Set Prolog a language for knowledge representation and reasoning based on the answer set/stable model semantics of logic programs [44, 45]. The language has roots in declarative programing [52, 65], the syntax and semantics of standard Prolog [24, 23], disjunctive databases [66, 67] and nonmonotonic logic
A Reductive Semantics for Counting and Choice in Answer Set Programming
"... In a recent paper, Ferraris, Lee and Lifschitz conjectured that the concept of a stable model of a firstorder formula can be used to treat some answer set programming expressions as abbreviations. We follow up on that suggestion and introduce an answer set programming language that defines the mean ..."
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Cited by 28 (19 self)
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In a recent paper, Ferraris, Lee and Lifschitz conjectured that the concept of a stable model of a firstorder formula can be used to treat some answer set programming expressions as abbreviations. We follow up on that suggestion and introduce an answer set programming language that defines the meaning of counting and choice by reducing these constructs to firstorder formulas. For the new language, the concept of a safe program is defined, and its semantic role is investigated. We compare the new language with the concept of a disjunctive program with aggregates introduced by Faber, Leone and Pfeifer, and discuss the possibility of implementing a fragment of the language by translating it into the input language of the answer set solver DLV. The language is also compared with cardinality constraint programs defined by Syrjänen.
Symmetric splitting in the general theory of stable models
, 2010
"... Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for smaller programs. This idea is extended here to the general theory of stable models that replaces traditional logic programs by arbitrary firstorder sentences and distinguishes between intensio ..."
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Cited by 26 (15 self)
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Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for smaller programs. This idea is extended here to the general theory of stable models that replaces traditional logic programs by arbitrary firstorder sentences and distinguishes between intensional and extensional predicates. We discuss two kinds of splitting: a set of intensional predicates can be split into subsets, and a formula can be split into its conjunctive terms.
Quantified equilibrium logic and hybrid rules
 In Proceedings ASP2007
, 2007
"... Abstract. In the ongoing discussion about combining rules and Ontologies on the Semantic Web a recurring issue is how to combine firstorder classical logic with nonmonotonic rule languages. Whereas several modular approaches to define a combined semantics for such hybrid knowledge bases focus mainl ..."
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Cited by 25 (7 self)
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Abstract. In the ongoing discussion about combining rules and Ontologies on the Semantic Web a recurring issue is how to combine firstorder classical logic with nonmonotonic rule languages. Whereas several modular approaches to define a combined semantics for such hybrid knowledge bases focus mainly on decidability issues, we tackle the matter from a more general point of view. In this paper we show how Quantified Equilibrium Logic (QEL) can function as a unified framework which embraces classical logic as well as disjunctive logic programs under the (open) answer set semantics. In the proposed variant of QEL we relax the unique names assumption, which was present in earlier versions of QEL. Moreover, we show that this framework elegantly captures the existing modular approaches for hybrid knowledge bases in a unified way. 1
Circumscriptive Event Calculus as Answer Set Programming
"... Recently, Ferraris, Lee and Lifschitz presented a general definition of a stable model that is similar to the definition of circumscription, and can even be characterized in terms of circumscription. In this paper, we show the opposite direction, which is, how to turn circumscription into the genera ..."
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Cited by 24 (8 self)
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Recently, Ferraris, Lee and Lifschitz presented a general definition of a stable model that is similar to the definition of circumscription, and can even be characterized in terms of circumscription. In this paper, we show the opposite direction, which is, how to turn circumscription into the general stable model semantics, and based on this, how to turn circumscriptive event calculus into answer set programs. The reformulation of the event calculus in answer set programming allows answer set solvers to be applied to event calculus reasoning, handling more expressive reasoning tasks than the current SATbased approach. Our experiments also show clear computational advantages of the answer set programming approach. 1
Twelve Definitions of a Stable Model
"... This is a review of some of the definitions of the concept of a stable model that have been proposed in the literature. These definitions are equivalent to each other, at least when applied to traditional Prologstyle programs, but there are reasons why each of them is valuable and interesting. A n ..."
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Cited by 23 (1 self)
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This is a review of some of the definitions of the concept of a stable model that have been proposed in the literature. These definitions are equivalent to each other, at least when applied to traditional Prologstyle programs, but there are reasons why each of them is valuable and interesting. A new characterization of stable models can suggest an alternative picture of the intuitive meaning of logic programs; or it can lead to new algorithms for generating stable models; or it can work better than others when we turn to generalizations of the traditional syntax that are important from the perspective of answer set programming; or it can be more convenient for use in proofs; or it can be interesting simply because it demonstrates a relationship between seemingly unrelated ideas.
System f2lp – computing answer sets of firstorder formulas
 In Procedings of International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR
, 2009
"... Abstract. We present an implementation of the general language of stable models proposed by Ferraris, Lee and Lifschitz. Under certain conditions, system f2lp turns a firstorder theory under the stable model semantics into an answer set program, so that existing answer set solvers can be used for c ..."
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Cited by 21 (13 self)
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Abstract. We present an implementation of the general language of stable models proposed by Ferraris, Lee and Lifschitz. Under certain conditions, system f2lp turns a firstorder theory under the stable model semantics into an answer set program, so that existing answer set solvers can be used for computing the general language. Quantifiers are first eliminated and then the resulting quantifierfree formulas are turned into rules. Based on the relationship between stable models and circumscription, f2lp can also serve as a reasoning engine for general circumscriptive theories. We illustrate how to use f2lp to compute the circumscriptive event calculus. 1
Stable models of formulas with intensional functions
 In Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR
"... In classical logic, nonBoolean fluents, such as the location of an object and the color of a ball, can be naturally described by functions, but this is not the case with the traditional stable model semantics, where the values of functions are predefined, and nonmonotonicity of the semantics is rela ..."
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Cited by 18 (11 self)
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In classical logic, nonBoolean fluents, such as the location of an object and the color of a ball, can be naturally described by functions, but this is not the case with the traditional stable model semantics, where the values of functions are predefined, and nonmonotonicity of the semantics is related to minimizing the extents of predicates but has nothing to do with functions. We extend the firstorder stable model semantics by Ferraris, Lee and Lifschitz to allow intensional functions. The new formalism is closely related to multivalued nonmonotonic causal logic, logic programs with intensional functions, and other extensions of logic programs with functions, while keeping similar properties as those of the firstorder stable model semantics. We show how to eliminate intensional functions in favor of intensional predicates and vice versa, and use these results to encode fragments of the language in the input language of ASP solvers and CSP solvers.
On loop formulas with variables
 In Proceedings of the International Conference on Knowledge Representation and Reasoning (KR
, 2008
"... Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary firstorder sentences. We show its relation to the idea of loop formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop f ..."
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Cited by 16 (6 self)
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Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary firstorder sentences. We show its relation to the idea of loop formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop formulas to disjunctive programs and to arbitrary firstorder sentences. We also extend the syntax of logic programs to allow explicit quantifiers, and define its semantics as a subclass of the new language of stable models by Ferraris et al. Such programs inherit from the general language the ability to handle nonmonotonic reasoning under the stable model semantics even in the absence of the unique name and the domain closure assumptions, while yielding more succinct loop formulas than the general language due to the restricted syntax. We also show certain syntactic conditions under which query answering for an extended program can be reduced to entailment checking in firstorder logic, providing a way to apply firstorder theorem provers to reasoning about nonHerbrand stable models.