Non-deterministic approximation fixpoint theory and its application in disjunctive logic programming

Jesse Heyninck*, Ofer Arieli, Bart Bogaerts

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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.

Original languageEnglish
Article number104110
Number of pages37
JournalArtificial Intelligence
Publication statusPublished - Jun 2024


  • Answer Set Programming
  • Approximation Fixpoint Theory
  • Knowledge Representation
  • Logic Programming


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