Approximation Fixpoint Theory (AFT) is an algebraic framework designed to study the semantics of non-monotonic logics. Despite its success, AFT is not readily applicable to higher-order definitions. To solve such an issue, we devise a formal mathematical framework employing concepts drawn from Category Theory. In particular, we make use of the notion of Cartesian closed category to inductively construct higher-order approximation spaces while preserving the structures necessary for the correct application of AFT. We show that this novel theoretical approach extends standard AFT to a higher-order environment, and generalizes the AFT setting of arXiv:1804.08335 . Under consideration in Theory and Practice of Logic Programming (TPLP).

翻译：逼近不动点理论（AFT）是一种用于研究非单调逻辑语义的代数框架。尽管该理论已取得显著成功，但其难以直接应用于高阶定义。为解决这一问题，我们构建了一个运用范畴论概念的正式数学框架。特别地，我们利用笛卡尔闭范畴的概念归纳地构造高阶逼近空间，同时保持正确应用AFT所需的结构。我们证明这一新颖的理论方法将标准AFT扩展至高阶环境，并推广了arXiv:1804.08335中的AFT设定。本文已提交至《逻辑编程理论与应用》（TPLP）审议。