A Reconstruction of Ex Falso Quodlibet via Quasi-Multiple-Conclusion Natural Deduction

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10455)

Abstract

This paper is intended to offer a philosophical analysis of the propositional intuitionistic logic formulated as \(\textit{NJ}\). This system has been connected to Prawitz and Dummett’s proof-theoretic semantics and its computational counterpart. The problem is, however, there has been no successful justification of ex falso quodlibet (EFQ): “From the absurdity ‘\(\bot \)’, an arbitrary formula follows.” To justify this rule, we propose a novel intuitionistic natural deduction with what we call quasi-multiple conclusion. In our framework, EFQ is no longer an inference deriving everything from ‘\(\bot \)’, but rather represents a “jump” inference from the absurdity to the other possibility.

Keywords

Ex Falso Quodlibet Intuitionistic logic Proof-theoretic semantics Curry–Howard correspondence Catch/throw mechanism 
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Notes

Acknowledgment

We appreciate the helpful comments of Atsushi Igarashi and Takuro Onishi that improved the presentation of this paper. We are also grateful to the anonymous referees for their helpful comments.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Graduate School of InformaticsKyoto UniversityKyotoJapan
  2. 2.Graduate School of LettersKyoto UniversityKyotoJapan

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