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arXiv · 2305.10846

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

Jesse Heyninck·Bart Bogaerts
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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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Jesse Heyninck, Bart Bogaerts. 2023-05-18. Non-deterministic approximation operators: ultimate operators, semi-equilibrium semantics and aggregates (full version). https://arxiv.org/abs/2305.10846

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