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The number of lines in Frege proofs with substitution

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Abstract.

We prove that for sufficiently large \(n\), there are tautologies of size \(O(n)\) that require proofs containing \(\Omega( n / \log n )\) lines in axiomatic systems of propositional logic based on the rules of substitution and detachment.

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Authors and Affiliations

  1. Department of Philosophy, University of Toronto, 215 Huron Street, 9th Floor, Toronto, Ontario, M5S 1A1, Canada , , , , , , CA

    Alasdair Urquhart

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  1. Alasdair Urquhart
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Received October 19, 1995

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Urquhart, A. The number of lines in Frege proofs with substitution. Arch Math Logic 37, 15–19 (1997). https://doi.org/10.1007/s001530050078

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  • DOI: https://doi.org/10.1007/s001530050078

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