Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to dealing with that allow to handle indefinite information, represented e.g. by disjunctive formulas. This is done by generalizing the main constructions and corresponding results of AFT to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.

中文翻译：

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非确定性逼近不动点理论及其在析取逻辑编程中的应用

近似不动点理论（AFT）是用于研究非单调逻辑语义的抽象通用代数框架。它提供了对非单调推理的不同形式主义语义的统一研究，例如逻辑编程、默认逻辑和自认知逻辑。在本文中，我们将 AFT 扩展到允许处理不确定信息，例如由析取公式表示的信息。这是通过将 AFT 的主要结构和相应结果推广到非确定性运算符来完成的，这些运算符的范围是元素集而不是单个元素。这种概括的适用性和有用性在析取逻辑编程的背景下得到了说明。