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

摘要

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.