A Sound and Complete Tableaux Calculus for Reichenbach’s Quantum Mechanics Logic

Journal of Philosophical Logic 53 (1):223-245 (2024)
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Abstract

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.

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Pablo Caballero
Universidad de Sevilla

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References found in this work

Philosophy of Physics: Quantum Theory.Tim Maudlin - 2019 - Princeton: Princeton University Press.
Philosophic foundations of quantum mechanics.Hans Reichenbach - 1944 - Mineola, N.Y.: Dover Publications.
An Introduction to Non-Classical Logic: From If to Is.Graham Priest - 2008 - Bulletin of Symbolic Logic 14 (4):544-545.

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