English

Non-deterministic approximation operators: ultimate operators, semi-equilibrium semantics and aggregates (full version)

Artificial Intelligence 2023-05-19 v1 Logic in Computer Science

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, i.e.\ 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 characterisations of disjunctive logic programs to disjunctive logic programs with aggregates.

Keywords

Cite

@article{arxiv.2305.10846,
  title  = {Non-deterministic approximation operators: ultimate operators, semi-equilibrium semantics and aggregates (full version)},
  author = {Jesse Heyninck and Bart Bogaerts},
  journal= {arXiv preprint arXiv:2305.10846},
  year   = {2023}
}

Comments

Paper presented at the 39th International Conference on Logic Programming (ICLP 2023)

R2 v1 2026-06-28T10:38:03.547Z