Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. Due to their first-order semantics, these languages (in their classical form) are not suitable for representing and handling uncertainty. A probabilistic extension of a light-weight DL was recently proposed for dealing with certain knowledge occurring in uncertain contexts. In this paper, we continue that line of research by introducing the Bayesian extension \BALC of the propositionally closed DL \ALC. We present a tableau-based procedure for deciding consistency, and adapt it to solve other probabilistic, contextual, and general inferences in this logic. We also show that all these problems remain \ExpTime-complete, the same as reasoning in the underlying classical \ALC.

中文翻译：

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概率描述逻辑 $\mathcal{BALC}$

描述逻辑 (DL) 是众所周知的知识表示形式，专注于术语知识的表示。由于它们的一阶语义，这些语言（以其经典形式）不适合表示和处理不确定性。最近提出了轻量级 DL 的概率扩展，用于处理发生在不确定环境中的某些知识。在本文中，我们通过引入命题闭 DL \ALC 的贝叶斯扩展 \BALC 来继续这一研究。我们提出了一个基于表格的程序来决定一致性，并对其进行调整以解决此逻辑中的其他概率、上下文和一般推理。我们还表明，所有这些问题仍然是 \ExpTime-complete，与基础经典 \ALC 中的推理相同。