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.

翻译：近似不动点理论（AFT）是一个抽象且通用的代数框架，用于研究非单调逻辑的语义。在近期工作中，AFT被推广至非确定性算子，即其值域为元素集合而非单个元素的算子。本文对非确定性AFT做出了三项进一步贡献：（1）定义并研究了非确定性算子的终极近似；（2）给出了Amendola等人提出的半均衡语义的代数化表述；（3）将析取逻辑程序的刻画推广至带聚合的析取逻辑程序。