Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary results on reasoning in a family of modal description logics obtained by combining ALC with non-normal modal operators. First, we provide a framework of terminating, correct, and complete tableau algorithms to check satisfiability of formulas in such logics with the semantics based on varying domains. We then investigate the satisfiability problems in fragments of these languages obtained by restricting the application of modal operators to formulas only, and interpreted on models with constant domains, providing tight complexity results.
翻译:非正常模式逻辑,根据一般关系语义学的周边模型来解释,这些非正常模式逻辑已经在若干领域应用,例如缩写、疏松和联合推理。我们在此介绍通过将ALC与非正常模式操作者结合而获得的一组模式描述逻辑逻辑的推理的初步结果。首先,我们提供了一个终止、正确和完整的表式算法框架,以检查这些逻辑中公式与基于不同域的语义学的相对性。然后,我们调查这些语言的碎片的可比较性问题,通过将模式操作者仅应用于公式,并按具有恒定域的模型加以解释,提供复杂程度极强的结果。