The transition semantics presented in Rumberg (J Log Lang Inf 25(1):77–108, 2016a) constitutes a fine-grained framework for modeling the interrelation of modality and time in branching time structures. In that framework, sentences of the transition language $$\mathcal {L}_\mathsf{t}$$Lt are evaluated on transition structures at pairs consisting of a moment and a set of transitions. In this paper, we provide a class of first-order definable Kripke structures that preserves $$\mathcal {L}_\mathsf{t}$$Lt-validity w.r.t. transition structures. As a consequence, for a certain fragment of $$\mathcal {L}_\mathsf{t}$$Lt, validity w.r.t. transition structures turns out to be axiomatizable. The result is then extended to the entire language $$\mathcal {L}_\mathsf{t}$$Lt by means of a quite natural ‘Henkin move’, i.e. by relaxing the notion of validity to bundled structures.

中文翻译：

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过渡结构的一阶可定义性

Rumberg (J Log Lang Inf 25(1):77–108, 2016a) 中提出的转换语义构成了一个细粒度的框架，用于对分支时间结构中的模态和时间的相互关系进行建模。在该框架中，转换语言 $$\mathcal {L}_\mathsf{t}$$Lt 的句子在由时刻和一组转换组成的成对转换结构上进行评估。在本文中，我们提供了一类一阶可定义的 Kripke 结构，它保留了 $$\mathcal {L}_\mathsf{t}$$Lt-validity wrt 转换结构。因此，对于 $$\mathcal {L}_\mathsf{t}$$Lt 的某个片段，有效性 wrt 转换结构结果是公理化的。然后通过非常自然的“亨金移动”将结果扩展到整个语言 $$\mathcal {L}_\mathsf{t}$$Lt，即