Approximation fixpoint theory (AFT) is an algebraic study of fixpoints of lattice operators that unifies various knowledge representation formalisms. In AFT, stratification of operators has been studied, essentially resulting in a theory that specifies when certain types of fixpoints can be computed stratum per stratum. Recently, novel types of fixpoints related to groundedness have been introduced in AFT. In this article, we study how those fixpoints behave under stratified operators. One recent application domain of AFT is the field of active integrity constraints (AICs). We apply our extended stratification theory to AICs and find that existing notions of stratification in AICs are covered by this general algebraic definition of stratification. As a result, we obtain stratification results for a large variety of semantics for AICs.

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近似不动点理论中的分层及其在主动完整性约束中的应用

近似不动点理论 (AFT) 是对格算子不动点的代数研究，它统一了各种知识表示形式。在 AFT 中，已经研究了算子的分层，本质上产生了一种理论，该理论指定了何时可以逐层计算某些类型的固定点。最近，新的固定点类型与接地气已在 AFT 中引入。在本文中，我们研究了这些固定点在分层运算符下的行为。AFT 最近的一个应用领域是主动完整性约束（AIC）。我们将扩展的分层理论应用于 AIC，并发现 AIC 中现有的分层概念包含在分层的一般代数定义中。结果，我们获得了 AIC 的各种语义的分层结果。