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

Jesse Heyninck, Bart Bogaerts
5/18/2023
cs.AIcs.LO

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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.

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Cite this paper

@article{heyninck2023nondeterministic,
  title  = {Non-deterministic approximation operators: ultimate operators, semi-equilibrium semantics and aggregates (full version)},
  author = {Jesse Heyninck and Bart Bogaerts},
  year   = {2023},
  eprint = {2305.10846},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2305.10846v1}
}

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