Reasoning about actual causes of observed effects is fundamental to the study of rationality. This important problem has been studied since the time of Aristotle, with formal mathematical accounts emerging recently. We live in a world where change due to actions can be both discrete and continuous, that is, hybrid. Yet, despite extensive research on actual causation, only few recent studies looked into causation with continuous change. Building on recent progress, in this paper we propose two definitions of primary cause in a hybrid action-theoretic framework, namely the hybrid temporal situation calculus. One of these is foundational in nature while the other formalizes causation through contributions, which can then be verified from a counterfactual perspective using a modified ``but-for'' test. We prove that these two definitions are indeed equivalent. We then show that our definitions of causation have some intuitively justifiable properties.

翻译：对观察到的效应的实际原因进行推理是理性研究的基石。这一重要问题自亚里士多德时代起便受到关注，直至近期才出现形式化的数学描述。我们所处的世界中，由行动引起的变化既可以是离散的，也可以是连续的，即混合的。然而，尽管关于实际因果关系的研究已相当广泛，近期仅有少数研究探讨了涉及连续变化的因果关系。基于最新进展，本文在混合行动理论框架——即混合时序情景演算——中提出了两种首要因果的定义。其中一种是基础性的定义，另一种则通过贡献度来形式化因果关系，并可通过改进的“若非”检验从反事实角度进行验证。我们证明了这两种定义实际上是等价的。随后，我们展示了所提出的因果定义具有若干直观上合理的性质。