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arXiv · 2211.17262

Non-Deterministic Approximation Fixpoint Theory and Its Application in Disjunctive Logic Programming

Jesse Heyninck·Ofer Arieli·Bart Bogaerts
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Abstract

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.

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Jesse Heyninck, Ofer Arieli, Bart Bogaerts. 2022-11-30. Non-Deterministic Approximation Fixpoint Theory and Its Application in Disjunctive Logic Programming. https://arxiv.org/abs/2211.17262

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