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

J.L.A. Heyninck, Bart Bogaerts

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

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
Pages (from-to)632-647
Number of pages16
JournalTheory and Practice of Logic Programming
Volume23
Issue number4
Early online date11 Jul 2023
DOIs
Publication statusPublished - Jul 2023

Keywords

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

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