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

机译:相对相似性逻辑是可以确定的:等式减少到DO〜2

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摘要

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:我们显示了相对相似性逻辑的可满足性问题的可判定性,该逻辑允许在不完整信息存在的情况下对对象进行分类。作为副作用,我们获得了此类相似逻辑的有限模型属性。证明技术包括减少可判定片段FO〜2的可满足性问题,与经典逻辑相等。尽管归约是从模态逻辑到经典逻辑的标准转换而来的,但我们的原始方法(例如处理原子性质的标称和根据归约中编码的成分进行分解)可以推广到更大的一类相对逻辑中,这为我们开辟了道路。有待进一步调查。

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