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Approximation fixpoint theory (AFT) is an abstract and general algebraicframework for studying the semantics of non-monotonic logics. In recent work,AFT was generalized to non-deterministic operators, i.e.\ operators whose rangeare sets of elements rather than single elements. In this paper, we make threefurther contributions to non-deterministic AFT: (1) we define and studyultimate approximations of non-deterministic operators, (2) we give analgebraic formulation of the semi-equilibrium semantics by Amendola, et al.,and (3) we generalize the characterisations of disjunctive logic programs todisjunctive logic programs with aggregates.

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