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Propositions in Prepositional Logic Provable Only by Indirect Proofs
Mathematical Logic Quarterly 44 (1):69-91 (1998)
Abstract
In this paper it is shown that addition of certain reductions to the standard cut removing reductions of deductions in prepositional logic makes prepositional logic non-normalizable. From this follows that some provable propositions in prepositional logic has no direct proofMy notes
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Citations of this work
Ekman’s Paradox.Peter Schroeder-Heister & Luca Tranchini - 2017 - Notre Dame Journal of Formal Logic 58 (4):567-581.
Proof-Theoretic Semantics, Self-Contradiction, and the Format of Deductive Reasoning.Peter Schroeder-Heister - 2012 - Topoi 31 (1):77-85.
How to Ekman a Crabbé-Tennant.Peter Schroeder-Heister & Luca Tranchini - 2018 - Synthese 199 (Suppl 3):617-639.
Normalizability, cut eliminability and paradox.Neil Tennant - 2016 - Synthese 199 (Suppl 3):597-616.
Non-transitive Correspondence Analysis.Yaroslav Petrukhin & Vasily Shangin - 2023 - Journal of Logic, Language and Information 32 (2):247-273.
References found in this work
Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
Natural Deduction: A Proof-Theoretical Study.Richmond Thomason - 1965 - Journal of Symbolic Logic 32 (2):255-256.
The Collected Papers of Gerhard Gentzen. [REVIEW]G. Kreisel - 1971 - Journal of Philosophy 68 (8):238-265.
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