@article{HEYNINCK2024104110,
title = {Non-deterministic approximation fixpoint theory and its application in disjunctive logic programming},
journal = {Artificial Intelligence},
volume = {331},
pages = {104110},
year = {2024},
issn = {0004-3702},
doi = {https://doi.org/10.1016/j.artint.2024.104110},
url = {https://www.sciencedirect.com/science/article/pii/S0004370224000468},
author = {Jesse Heyninck and Ofer Arieli and Bart Bogaerts},
keywords = {Logic Programming, Answer Set Programming, Approximation Fixpoint Theory, Knowledge Representation},
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.}
}