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

• URL: http://arxiv.org/abs/2305.10846v1
• Date: Thu, 18 May 2023 09:59:12 GMT
• Title: Non-deterministic approximation operators: ultimate operators, semi-equilibrium semantics and aggregates (full version)
• Authors: Jesse Heyninck and Bart Bogaerts
• Abstract summary: We make three further contributions to non-deterministic AFT. We define and study ultimate approximations of non-deterministic operators. We generalize the characterisations of disjunctive logic programs to disjunctive logic programs with aggregates.
• Score: 13.249453757295083
• License: http://creativecommons.org/licenses/by/4.0/
• 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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