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

Jesse Heyninck, Bart Bogaerts

Research output: Contribution to journalArticlepeer-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
Pages (from-to)632-647
Number of pages16
JournalTheory and Practice of Logic Programming
Issue number4
Publication statusPublished - 2023

Bibliographical note

Funding Information:
This work was partially supported by Fonds Wetenschappelijk Onderzoek – Vlaanderen (project G0B2221N) and the Flemish Government (Onderzoeksprogramma Artificiële Intelligentie (AI) Vlaanderen).

Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press.


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