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Relative Similarity Logics are Decidable: Reduction to FO~2 with Equality

机译:相对相似度逻辑是可解析的:减少与平等执行〜2

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We show the decidability of the satisfiability problem for relative similarity logics that allow classification of objects in presence of incomplete inforamtion. As a side-effect, we obtain a finite model property for such similarity logics. The proof technique consists of reductions into the satisfiability problem for the decidable fragment FO~2 with equality from classical logic. Although the reductions stem from the standard translation from modal logic into classical logic, our original approach (for instance handling nominals for atomic properties and decomposition in terms of components encoded in the reduction) can be generalized to a larger class of relative logics, opening ground for further investigations.
机译:我们展示了相对相似逻辑的可靠性问题的可解锁性,允许在存在不完整的Inforamtion中分类对象的分类。作为副作用,我们获得了用于此类相似逻辑的有限模型属性。证明技术包括降低到具有古典逻辑等平等的可解除的片段的可解除片段的可靠性问题。虽然减少源于从模态逻辑到经典逻辑的标准转换,但我们的原始方法(例如在减少中编码的组件中处理原子特性和分解的名义)可以推广到更大类别的相对逻辑,开口地进一步调查。

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