The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible to extend functional programming languages with new features via type theory, while from the semantics perspective, several logics for reasoning about dynamical systems and several semantics for logic programming have their roots in this framework. We consider several axiomatic systems for intuitionistic linear temporal logic and show that each of these systems is sound for a class of structures based either on Kripke frames or on dynamic topological systems. We provide two distinct interpretations of “henceforth”, both of which are natural intuitionistic variants of the classical one. We completely establish the order relation between the semantically defined logics based on both interpretations of “henceforth” and, using our soundness results, show that the axiomatically defined logics enjoy the same order relations.

中文翻译：

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探索直觉时间逻辑的丛林

在过去的几年里，直觉时间逻辑在计算机科学和人工智能中的重要性变得越来越明显。从证明论的角度来看，直觉主义的时序逻辑使得通过类型论扩展具有新特性的函数式编程语言成为可能，而从语义的角度来看，用于推理动态系统的几种逻辑和用于逻辑编程的几种语义都有其根源在这个框架内。我们考虑了几个用于直觉线性时间逻辑的公理系统，并表明这些系统中的每一个对于基于 Kripke 框架或动态拓扑系统的一类结构都是合理的。我们对“从此以后”提供了两种不同的解释，这两种解释都是经典解释的自然直觉变体。