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

Abstract

Approximation fixpoint theory (AFT) constitutes 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 non-deterministic constructs such as disjunctive information. This is done by generalizing the main constructions and corresponding results 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.

Conditional Abstract Dialectical Frameworks

“…Therefore, the Γfunction might contain multiple interpretations which all do an equally good job of aligning the truth values of statements φ with their respective conditions ψ. Thus, Γ Π is defined as a non-deterministic operator (Pelov and Truszczynski 2004;Heyninck and Arieli 2021), in the sense that a single interpretation v might give rise to a non-singleton set of interpretations {v 1 , . .…”