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arXiv 2502.20751math.LOcs.LO
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有序模型的终止混合表aux

Terminating Hybrid Tableaus for Ordered Models

Yuki Nishimura

AI总结:

本文提出三种终止表aux系统,用于处理严格偏序、无界严格偏序和偏序模型,通过引入名义来描述二元关系属性,提升部分序处理能力。

摘要:

混合逻辑通过引入称为名义的特殊命题扩展模态逻辑,每个名义仅在模型的一个状态为真。这使我们能够描述二元关系的一些属性,如非反射性和反对称性,这些对于处理偏序至关重要。我们提出了三种终止表aux系统,这些系统在严格偏序、无界严格偏序和偏序模型上是完备的。

英文摘要:

Hybrid logic extends modal logic with special propositions called nominals, each of which is true at only one state in a model. This enables us to describe some properties of binary relations, such as irreflexivity and anti-symmetry, which are essential to treat partial orders. We present terminating tableau calculi complete with respect to models whose accessibility relations are strictly partially ordered, unbounded strictly partially ordered, and partially ordered.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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