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A Gentzen-type calculus of sequents for single-operator propositional logic*
Published online by Cambridge University Press: 12 March 2014
Extract
The following describes a calculus of sequents (SLK) patterned after the calculus LK of Gentzen in [1] but restricted to the formulas of propositional logic and modified so that the only connective is the Sheffer stroke. The ‘elimination theorem’ (Hauptsatz) is proved for SLK and a decision procedure is specified for determining whether a given formula in stroke notation is tautologous. In addition, SLK is proved consistent and complete. Subsequent remarks indicate briefly how the calculus can be modified so as to employ the dagger as the only connective.
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- Copyright © Association for Symbolic Logic 1967
Footnotes
I wish to thank the referee for suggesting the general direction this paper should take and for commenting specifically upon several points.
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