Recently we established an analog of Gabbay's separation theorem about linear temporal logic (LTL) for the extension of Moszkowski's discrete time propositional Interval Temporal Logic (ITL) by two sets of expanding modalities, namely the unary neighbourhood modalities and the binary weak inverses of ITL's operator. One of the many useful applications of separation in LTL is the concise proof of LTL's expressive completeness wrt the monadic first-order theory of it enables. In this paper we show how our separation theorem about ITL facilitates a similar proof of the expressive completeness of ITL with expanding modalities wrt the monadic first- and second-order theories of .

中文翻译：

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通过扩展模态分离离散时间间隔时序逻辑的表达完整性

最近，我们建立了关于线性时态逻辑（LTL）的 Gabbay 分离定理的类比，用于通过两组扩展模态（即一元邻域模态和 ITL 算子的二元弱逆）来扩展 Moszkowski 的离散时间命题区间时态逻辑（ITL） 。LTL 中分离的许多有用应用之一是对 LTL 的一元一阶理论的表达完整性的简洁证明。在本文中，我们展示了关于 ITL 的分离定理如何通过关于 的单子一阶和二阶理论的扩展模态来促进 ITL 表达完整性的类似证明。