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

TL;DR

This paper extends approximation fixpoint theory to non-deterministic operators, enabling better semantic analysis of disjunctive logic programming by handling indefinite information through set-valued constructs.

Contribution

It introduces a non-deterministic extension of AFT, generalizing core concepts to sets of elements, and applies this to improve understanding of disjunctive logic programming semantics.

Findings

Generalized AFT to non-deterministic operators

Enhanced semantic analysis for disjunctive logic programming

Illustrated applicability in handling indefinite information

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.