Strong and uniform equivalence of nonmonotonic theories - An algebraic approach

Mirosław Truszczyński

doi:10.1007/s10472-007-9049-2

Strong and uniform equivalence of nonmonotonic theories - An algebraic approach

Mirosław Truszczyński

Computer Science

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

We show that the concepts of strong and uniform equivalence of logic programs can be generalized to an abstract algebraic setting of operators on complete lattices. Our results imply characterizations of strong and uniform equivalence for several nonmonotonic logics including logic programming with aggregates, default logic and a version of autoepistemic logic.

Original language	English
Pages (from-to)	245-265
Number of pages	21
Journal	Annals of Mathematics and Artificial Intelligence
Volume	48
Issue number	3-4
DOIs	https://doi.org/10.1007/s10472-007-9049-2
State	Published - Dec 2006

Bibliographical note

Funding Information:
This work was partially supported by the NSF grant IIS-0325063.

Keywords

Autoepistemic logic
Default logic
Nonmonotonic theories

ASJC Scopus subject areas

Artificial Intelligence
Applied Mathematics

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10.1007/s10472-007-9049-2

Cite this

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title = "Strong and uniform equivalence of nonmonotonic theories - An algebraic approach",

abstract = "We show that the concepts of strong and uniform equivalence of logic programs can be generalized to an abstract algebraic setting of operators on complete lattices. Our results imply characterizations of strong and uniform equivalence for several nonmonotonic logics including logic programming with aggregates, default logic and a version of autoepistemic logic.",

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author = "Miros{\l}aw Truszczy{\'n}ski",

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N2 - We show that the concepts of strong and uniform equivalence of logic programs can be generalized to an abstract algebraic setting of operators on complete lattices. Our results imply characterizations of strong and uniform equivalence for several nonmonotonic logics including logic programming with aggregates, default logic and a version of autoepistemic logic.

AB - We show that the concepts of strong and uniform equivalence of logic programs can be generalized to an abstract algebraic setting of operators on complete lattices. Our results imply characterizations of strong and uniform equivalence for several nonmonotonic logics including logic programming with aggregates, default logic and a version of autoepistemic logic.

KW - Autoepistemic logic

KW - Default logic

KW - Nonmonotonic theories

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JO - Annals of Mathematics and Artificial Intelligence

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IS - 3-4

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Strong and uniform equivalence of nonmonotonic theories - An algebraic approach

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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