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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Vydané v:	Artificial intelligence Ročník 331; s. 104110
Hlavní autori:	Heyninck, Jesse, Arieli, Ofer, Bogaerts, Bart
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 01.06.2024
Predmet:	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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Popis
Shrnutí:	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