@conference{420, author = {Jesse Heyninck and Ofer Arieli}, title = {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.}, year = {2021}, journal = {18th International Conference on Principles of Knowledge Representation and Reasoning}, chapter = {334-344}, month = {03/11-12/11}, publisher = {IJCAI Organization}, address = {Online}, isbn = {978-1-956792-99-7}, url = {https://proceedings.kr.org/2021/32/}, doi = {10.24963/kr.2021/32}, }