In 1944 Hans Reichenbach developed a three-valued propositional logic (RQML) in order to account for certain causal anomalies in quantum mechanics. In this logic, the truth-value indeterminate is assigned to those statements describing physical phenomena that cannot be understood in causal terms. However, Reichenbach did not develop a deductive calculus for this logic. The aim of this paper is to develop such a calculus by means of First Degree Entailment logic (FDE) and to prove it sound and complete with respect to RQML semantics. In Section 1 we explain the main physical and philosophical motivations of RQML. Next, in Sections 2 and 3, respectively, we present RQML and FDE syntax and semantics and explain the relation between both logics. Section 4 introduces \(\varvec{\mathcal {Q}}\) calculus, an FDE-based tableaux calculus for RQML. In Section 5 we prove that \(\varvec{\mathcal {Q}}\) calculus is sound and complete with respect to RQML three-valued semantics. Finally, in Section 6 we consider some of the main advantages of \(\varvec{\mathcal {Q}}\) calculus and we apply it to Reichenbach’s analysis of causal anomalies.

1944 年，Hans Reichenbach 开发了三值命题逻辑 (RQML)，以解释量子力学中的某些因果异常。在这种逻辑中，真值不确定性被分配给那些描述无法用因果术语理解的物理现象的陈述。然而，赖兴巴赫并没有为这种逻辑发展出演绎演算。本文的目的是通过一级蕴涵逻辑 (FDE) 开发这样的演算，并证明其在 RQML 语义方面的合理性和完整性。在第 1 节中，我们解释 RQML 的主要物理和哲学动机。接下来，在第 2 节和第 3 节中，我们分别介绍 RQML 和 FDE 语法和语义，并解释两种逻辑之间的关系。第 4 节介绍\(\varvec{\mathcal {Q}}\)微积分，这是一种基于 FDE 的 RQML 表格微积分。在第 5 节中，我们证明\(\varvec{\mathcal {Q}}\)微积分对于 RQML 三值语义来说是合理且完整的。最后，在第 6 节中，我们考虑了\(\varvec{\mathcal {Q}}\)微积分的一些主要优点，并将其应用于 Reichenbach 对因果异常的分析。