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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Veröffentlicht in:	Artificial intelligence Jg. 331; S. 104110
Hauptverfasser:	Heyninck, Jesse, Arieli, Ofer, Bogaerts, Bart
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Elsevier B.V 01.06.2024
Schlagworte:	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
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Zusammenfassung:	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