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14
Logic programs with abstract constraint atoms
 In Proceedings of the 19th National Conference on Artificial Intelligence (AAAI04
, 2004
"... We propose and study extensions of logic programming with constraints represented as generalized atoms of the form C(X), where X is a finite set of atoms and C is an abstract constraint (formally, a collection of sets of atoms). Atoms C(X) are satisfied by an interpretation (set of atoms) M, if M ∩ ..."
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Cited by 22 (5 self)
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We propose and study extensions of logic programming with constraints represented as generalized atoms of the form C(X), where X is a finite set of atoms and C is an abstract constraint (formally, a collection of sets of atoms). Atoms C(X) are satisfied by an interpretation (set of atoms) M, if M ∩ X ∈ C. We focus here on monotone constraints, that is, those collections C that are closed under the superset. They include, in particular, weight (or pseudoboolean) constraints studied both by the logic programming and SAT communities. We show that key concepts of the theory of normal logic programs such as the onestep provability operator, the semantics of supported and stable models, as well as several of their properties including complexity results, can be lifted to such case.
Managing uncertainty and vagueness in description logics, logic programs and description logic programs
, 2008
"... Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages. Our aim is to overview basic concepts on representing uncertain and vague knowledge in current Semantic Web ontology and rule languages (and their combination). ..."
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Cited by 16 (5 self)
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Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages. Our aim is to overview basic concepts on representing uncertain and vague knowledge in current Semantic Web ontology and rule languages (and their combination).
Semantics of disjunctive programs with monotone aggregates  an operatorbased approach
 In: NMR
, 2004
"... All major semantics of normal logic programs and normal logic programs with aggregates can be described as fixpoints of the onestep provability operator or of operators that can be derived from it. No such systematic operatorbased approach to semantics of disjunctive logic programs has been develo ..."
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Cited by 14 (1 self)
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All major semantics of normal logic programs and normal logic programs with aggregates can be described as fixpoints of the onestep provability operator or of operators that can be derived from it. No such systematic operatorbased approach to semantics of disjunctive logic programs has been developed so far. This paper is the first step in this direction. We formalize the concept of onestepprovability for disjunctive logic programs by means of nondeterministic operators on the lattice of interpretations. We establish characterizations of models, minimal models, supported models and stable models of disjunctive logic programs in terms of prefixpoints and fixpoints of nondeterministic immediateconsequence operators and their extensions to the fourvalued setting. We develop our results for programs in propositional language extended with monotone aggregate atoms. For the most part, our concepts, results and proof techniques are algebraic, which opens a possibility for further generalizations to the abstract algebraic setting of nondeterministic operators on complete lattices.
Ultimate approximation and its application in nonmonotonic knowledge representation systems
, 2004
"... ..."
Properties and applications of programs with monotone and convex constraints
 J. ARTIFICIAL INTELLIGENCE RESEARCH
, 2006
"... We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations, tight programs and Fages Lemma, program completion and loop ..."
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Cited by 12 (0 self)
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We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations, tight programs and Fages Lemma, program completion and loop formulas. Our results provide an abstract account of properties of some recent extensions of logic programming with aggregates, especially the formalism of lparse programs. They imply a method to compute stable models of lparse programs by means of offtheshelf solvers of pseudoboolean constraints, which is often much faster than the smodels system.
Logic programs with monotone cardinality atoms
 In Proc. LPNMR2004
, 2004
"... Abstract. We investigate mcaprograms, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a nonnegative integer and X is a finite set of propositional atoms. We develop a theory of mcaprograms. We demonstrate that the operational concept of the one ..."
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Cited by 7 (0 self)
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Abstract. We investigate mcaprograms, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a nonnegative integer and X is a finite set of propositional atoms. We develop a theory of mcaprograms. We demonstrate that the operational concept of the onestep provability operator generalizes to mcaprograms, but the generalization involves nondeterminism. Our main results show that the formalism of mcaprograms is a common generalization of (1) normal logic programming with its semantics of models, supported models and stable models, (2) logic programming with cardinality atoms and with the semantics of stable models, as defined by Niemelä, Simons and Soininen, and (3) of disjunctive logic programming with the possiblemodel semantics of Sakama and Inoue. 1
Logic Programming for Knowledge Representation
, 2007
"... This note provides background information and references to the tutorial on recent research developments in logic programming inspired by need of knowledge representation. ..."
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Cited by 7 (0 self)
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This note provides background information and references to the tutorial on recent research developments in logic programming inspired by need of knowledge representation.
Connecting firstorder ASP and the logic FO(ID) through reducts
 In: Correct Reasoning: Essays on LogicBased AI in Honor of Vladimir Lifschitz
, 2012
"... on his 65th birthday! Abstract. Recently, an answerset programming (ASP) formalism of logic programing with the answerset semantics has been extended to the full firstorder setting. Earlier an extension of firstorder logic with inductive definitions, the logic FO(ID), was proposed as a knowledge ..."
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Cited by 5 (1 self)
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on his 65th birthday! Abstract. Recently, an answerset programming (ASP) formalism of logic programing with the answerset semantics has been extended to the full firstorder setting. Earlier an extension of firstorder logic with inductive definitions, the logic FO(ID), was proposed as a knowledge representation formalism and developed as an alternative ASP language. We present characterizations of these formalisms in terms of concepts of infinitary propositional logic. We use them to find a direct connection between the firstorder ASP and the logic FO(ID) under some restrictions on the form of theories (programs) considered. 1
Approximate wellfounded semantics, query answering and generalized normal logic programs over lattices
, 2008
"... Abstract The management of imprecise information in logic programs becomes important whenever the real world information to be represented is of an imperfect nature and the classical crisp true, false approximation is not adequate. In this work, we consider normal logic programs over complete lattic ..."
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Cited by 1 (0 self)
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Abstract The management of imprecise information in logic programs becomes important whenever the real world information to be represented is of an imperfect nature and the classical crisp true, false approximation is not adequate. In this work, we consider normal logic programs over complete lattices, where computable truth combination functions may appear in the rule bodies to manipulate truth values and we will provide a topdown query answering procedure. Keywords Logic programming · Nonmonotonic logic · Manyvalued logic
Semantics of Disjunctive Programs with Monotone Aggregates 
"... All major semantics of normal logic programs and normal logic programs with aggregates can be described as fixpoints of the onestep provability operator or of operators that can be derived from it. No such systematic operatorbased approach to semantics of disjunctive logic programs has been d ..."
Abstract
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All major semantics of normal logic programs and normal logic programs with aggregates can be described as fixpoints of the onestep provability operator or of operators that can be derived from it. No such systematic operatorbased approach to semantics of disjunctive logic programs has been developed so far. This paper is the first step in this direction.