Description logics have been extended in a number of ways to support defeasible reasoning in the KLM tradition. Such features include preferential or rational defeasible concept inclusion, and defeasible roles in complex concept descriptions. Semantically, defeasible subsumption is obtained by means of a preference order on objects, while defeasible roles are obtained by adding a preference order to role interpretations. In this paper, we address an important limitation in defeasible extensions of description logics, namely the restriction in the semantics of defeasible concept inclusion to a single preference order on objects. We do this by inducing a modular preference order on objects from each modular preference order on roles, and using these to relativise defeasible subsumption. This yields a notion of contextualised rational defeasible subsumption, with contexts described by roles. We also provide a semantic construction for rational closure and a method for its computation, and present a correspondence result between the two.

中文翻译：

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可废止 A 的上下文有理闭包 ℒ C $\mathcal {ALC}$

描述逻辑已以多种方式扩展，以支持 KLM 传统中的可废止推理。这些特征包括优先或合理的可废止概念包含，以及在复杂概念描述中的可废止角色。在语义上，可废止的包含是通过对对象的偏好顺序获得的，而可废止的角色是通过在角色解释中添加偏好顺序来获得的。在本文中，我们解决了描述逻辑的可废止扩展的一个重要限制，即可废止概念包含的语义限制对对象的单一偏好顺序。我们通过从角色的每个模块化偏好顺序中引入对象的模块化偏好顺序来做到这一点，并使用这些来相对化可废止的包含。这产生了上下文化的理性可废止的概念，上下文由角色描述。我们还提供了有理闭包的语义构造及其计算方法，并给出了两者之间的对应结果。