2022/11/30 by Jesse Heyninck, Heyninck, Jesse, Ofer Arieli +3 · 2 citations
Computer Science · #Advanced Algebra and Logic #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Formal Methods in Verification #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.2211.17262
openalex publication_date 2022/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.