We continue our investigation into hybrid polyadic multi-sorted logic with a focus on expresivity related to the operational and axiomatic semantics of rogramming languages, and relations with first-order logic. We identify a fragment of the full logic, for which we prove sound and complete deduction and we show that it is powerful enough to represent both the programs and their semantics in an uniform way. Although weaker than other hybrid systems previously developed, this system is expected to have better computational properties. Finally, we provide a standard translation from full hybrid many-sorted logic to first-order logic.

中文翻译：

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多排序混合模态语言

我们继续研究混合多元多排序逻辑，重点关注与编程语言的操作和公理语义相关的表达性，以及与一阶逻辑的关系。我们确定了完整逻辑的一个片段，为此我们证明了合理和完整的推论，并且我们证明它足够强大，可以以统一的方式表示程序及其语义。尽管比以前开发的其他混合系统弱，但预计该系统具有更好的计算特性。最后，我们提供了从完全混合多排序逻辑到一阶逻辑的标准转换。