Non-deterministic Approximation Operators: Ultimate Operators, Semi-equilibrium Semantics, and Aggregates

J.L.A. Heyninck, Bart Bogaerts

Research output: Contribution to journalArticleAcademicpeer-review


Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, that is, operators whose range are sets of elements rather than single elements. In this paper, we make three further contributions to non-deterministic AFT: (1) we define and study ultimate approximations of non-deterministic operators, (2) we give an algebraic formulation of the semi-equilibrium semantics by Amendola et al., and (3) we generalize the characterizations of disjunctive logic programs to disjunctive logic programs with aggregates.
Original languageEnglish
Number of pages16
JournalTheory and Practice of Logic Programming
Issue number4
Early online date11 Jul 2023
Publication statusPublished - Jul 2023


  • approximation fixpoint theory
  • disjunctive logic programming
  • semi-equilibrium semantics


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