Non-deterministic approximation fixpoint theory and its application in disjunctive logic programming

Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In...

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Bibliographic Details
Published in:Artificial intelligence Vol. 331; p. 104110
Main Authors: Heyninck, Jesse, Arieli, Ofer, Bogaerts, Bart
Format: Journal Article
Language:English
Published: Elsevier B.V 01.06.2024
Subjects:
Answer Set Programming
Approximation Fixpoint Theory
Knowledge Representation
Logic Programming
Knowledge Representation
Approximation Fixpoint Theory
Logic Programming
Answer Set Programming
ISSN:0004-3702, 1872-7921
Online Access:Get full text
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Summary:Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to dealing with non-deterministic constructs that allow to handle indefinite information, represented e.g. by disjunctive formulas. This is done by generalizing the main constructions and corresponding results of AFT to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.
ISSN:0004-3702
1872-7921
DOI:10.1016/j.artint.2024.104110