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Sequential Fuzzy Description Logic: Reasoning for Fuzzy Knowledge Bases with Sequential Information

机译：顺序模糊描述逻辑：具有顺序信息的模糊知识库的推理

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摘要

Description logics are known to be a family of logic-based knowledge representation formalisms, and fuzzy description logics are expressive description logics for representing and handling fuzzy (vague or imprecise) knowledge bases. A sequential fuzzy description logic, which is introduced in this paper, is an extended fuzzy description logic where a sequence modal operator is introduced. In this paper, a translation from the proposed sequential fuzzy description logic to a standard fuzzy description logic is defined. Further, a theorem for embedding the sequential fuzzy description logic into the standard fuzzy description logic is proved using this translation. A theorem for relative decidability of the sequential fuzzy description logic with respect to the standard fuzzy description logic is established using the embedding theorem. The proposed logic and translation are intended for effective handling of fuzzy knowledge bases with sequential information (i.e., information expressed as sequences). Moreover, using the translation, existing methods and algorithms for the standard fuzzy description logic can be reused to effectively handle fuzzy knowledge bases with sequential information described by the sequential fuzzy description logic.
机译：描述逻辑被称为基于逻辑的知识表示形式主义的系列，模糊描述逻辑是表示和处理模糊（模糊或不精确）知识库的逻辑的表现力描述逻辑。在本文中介绍的顺序模糊描述逻辑是一个扩展的模糊描述逻辑，其中介绍了序列模态运算符。在本文中，定义了所提出的顺序模糊描述逻辑到标准模糊描述逻辑的转换。此外，使用该转换证明了用于将顺序模糊描述逻辑嵌入到标准模糊描述逻辑中的定理。使用嵌入定理建立了关于标准模糊描述逻辑的顺序模糊描述逻辑的相对可解密性的定理。所提出的逻辑和翻译旨在有效处理具有顺序信息的模糊知识库（即，作为序列表示的信息）。此外，使用翻译，标准模糊描述逻辑的现有方法和算法可以重复使用，以有效地处理具有由顺序模糊描述逻辑描述的顺序信息的模糊知识库。

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