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Non-deterministic approximation fixpoint theory and its application in disjunctive logic programming
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DOI：10.1016/j.artint.2024.104110.png)
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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.
Keyword:
Logic Programming
Answer Set Programming
Approximation Fixpoint Theory
Knowledge Representation
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