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

• URL: http://arxiv.org/abs/2211.17262v2
• Date: Thu, 1 Dec 2022 08:58:45 GMT
• Title: Non-Deterministic Approximation Fixpoint Theory and Its Application in Disjunctive Logic Programming
• Authors: Jesse Heyninck and Ofer Arieli and Bart Bogaerts
• Abstract summary: Approximation fixpoint theory is a framework for studying the semantics of nonmonotonic logics. We extend AFT to dealing with non-deterministic constructs that allow to handle indefinite information. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.
• Score: 11.215352918313577
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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