Logic and Language


Ryosuke Igarashi (Kyoto University): A Reconstruction of Ex Falso Quodlibet via Quasi-Multiple-Conclusion Natural Deduction


Speaker: Ryosuke Igarashi (Kyoto University)
Title: A Reconstruction of Ex Falso Quodlibet via Quasi-Multiple-Conclusion Natural Deduction
Date:
Time: 16:00 - 17:30
Location: ILLC seminar room, F1.15

This paper is intended to offer a philosophical analysis of the propositional intuitionistic logic formulated as 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 ‘⊥’, 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 ‘⊥’, but rather represents a “jump” inference from the absurdity to the other possibility. The paper is joint work with Yosuke Fukuda.