Revisiting Reichenbach’s logic

Estrada-González, Luis; Cano-Jorge, Fernando

doi:10.1007/s11229-021-03313-2

Synthese

2021

DOI: 10.1007/s11229-021-03313-2

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Revisiting Reichenbach’s logic

Luis Estrada-González

Fernando Cano-Jorge

Abstract: In this paper we show that, when analyzed with contemporary tools in logic—such as Dunn-style semantics, Reichenbach’s three-valued logic exhibits many interesting features, and even new responses to some of the old objections to it can be attempted. Also, we establish some connections between Reichenbach’s three-valued logic and some contra-classical logics.

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Cited by 2 publications

References 26 publications

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

Caballero,

Valencia

2023

J Philos Logic

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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 $$\varvec{\mathcal {Q}}$$ Q calculus, an FDE-based tableaux calculus for RQML. In Section 5 we prove that $$\varvec{\mathcal {Q}}$$ 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 $$\varvec{\mathcal {Q}}$$ Q calculus and we apply it to Reichenbach’s analysis of causal anomalies.

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

Caballero,

Valencia

2023

J Philos Logic

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Dunn Semantics for Contra-Classical Logics

Estrada-González

2022

Electron. Proc. Theor. Comput. Sci.

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In this paper I show, with a rich and systematized diet of examples, that many contra-classical logics can be presented as variants of FDE, obtained by modifying at least one of the truth or falsity conditions of some connective. Then I argue that using Dunn semantics provides a clear understanding of the source of contra-classicality, namely, connectives that have either the classical truth or the classical falsity condition of another connective. This requires a fine-grained analysis of the sorts of modifications that can be made to an evaluation condition, analysis which I offer here as well.

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Revisiting Reichenbach’s logic

Cited by 2 publications

References 26 publications

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

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

Dunn Semantics for Contra-Classical Logics

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