Logic programs with monotone cardinality atoms

Victor W. Marek; Ilkka Niemelä; Miroslaw Truszczyński

Logic programs with monotone cardinality atoms

Victor W. Marek, Ilkka Niemelä, Miroslaw Truszczyński

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

13 Scopus citations

Abstract

We investigate mca-programs, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a non-negative integer and X is a finite set of propositional atoms. We develop a theory of mca-programs. We demonstrate that the operational concept of the one-step provability operator generalizes to mca-programs, but the generalization involves nondeterminism. Our main results show that the formalism of mca-programs 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 possible-model semantics of Sakama and Inoue.

Original language	English
Title of host publication	Logic Programming and Nonmonotonic Reasoning
Editors	Ilkka Niemela, Vladimir Lifschitz
Pages	154-166
Number of pages	13
ISBN (Electronic)	354020721X, 9783540207214
State	Published - 2004
Event	7th International Conference on Logic Programming and Nonmonotonic Reasoning , LPNMR 2004 - Fort Lauderdale, United States Duration: Jan 6 2004 → Jan 8 2004

Publication series

Name	Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)
Volume	2923
ISSN (Print)	0302-9743

Conference

Conference	7th International Conference on Logic Programming and Nonmonotonic Reasoning , LPNMR 2004
Country/Territory	United States
City	Fort Lauderdale
Period	1/6/04 → 1/8/04

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2004.

Funding

Funders	Funder number
Suomen Akatemia	53695
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	IIS-0325063, IIS-0097278
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	0325063

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Cite this

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title = "Logic programs with monotone cardinality atoms",

abstract = "We investigate mca-programs, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a non-negative integer and X is a finite set of propositional atoms. We develop a theory of mca-programs. We demonstrate that the operational concept of the one-step provability operator generalizes to mca-programs, but the generalization involves nondeterminism. Our main results show that the formalism of mca-programs 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 Niemel{\"a}, Simons and Soininen, and (3) of disjunctive logic programming with the possible-model semantics of Sakama and Inoue.",

author = "Marek, \{Victor W.\} and Ilkka Niemel{\"a} and Miroslaw Truszczy{\'n}ski",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2004.; 7th International Conference on Logic Programming and Nonmonotonic Reasoning , LPNMR 2004 ; Conference date: 06-01-2004 Through 08-01-2004",

year = "2004",

language = "English",

series = "Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)",

pages = "154--166",

editor = "Ilkka Niemela and Vladimir Lifschitz",

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Marek, VW, Niemelä, I & Truszczyński, M 2004, Logic programs with monotone cardinality atoms. in I Niemela & V Lifschitz (eds), Logic Programming and Nonmonotonic Reasoning. Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science), vol. 2923, pp. 154-166, 7th International Conference on Logic Programming and Nonmonotonic Reasoning , LPNMR 2004, Fort Lauderdale, United States, 1/6/04.

Logic programs with monotone cardinality atoms. / Marek, Victor W.; Niemelä, Ilkka; Truszczyński, Miroslaw.
Logic Programming and Nonmonotonic Reasoning. ed. / Ilkka Niemela; Vladimir Lifschitz. 2004. p. 154-166 (Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science); Vol. 2923).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Logic programs with monotone cardinality atoms

AU - Marek, Victor W.

AU - Niemelä, Ilkka

AU - Truszczyński, Miroslaw

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N2 - We investigate mca-programs, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a non-negative integer and X is a finite set of propositional atoms. We develop a theory of mca-programs. We demonstrate that the operational concept of the one-step provability operator generalizes to mca-programs, but the generalization involves nondeterminism. Our main results show that the formalism of mca-programs 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 possible-model semantics of Sakama and Inoue.

AB - We investigate mca-programs, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a non-negative integer and X is a finite set of propositional atoms. We develop a theory of mca-programs. We demonstrate that the operational concept of the one-step provability operator generalizes to mca-programs, but the generalization involves nondeterminism. Our main results show that the formalism of mca-programs 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 possible-model semantics of Sakama and Inoue.

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M3 - Conference contribution

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BT - Logic Programming and Nonmonotonic Reasoning

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ER -

Logic programs with monotone cardinality atoms

Abstract

Publication series

Conference

Bibliographical note

Funding

ASJC Scopus subject areas

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