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Condensed detachment is complete for relevance logic: A computer-aided proof

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Abstract

The condensed detachment ruleD is a combination of modus ponens with a minimal amount of substitution. EarlierD has been shown to be complete for intuitionistic and classical implicational logic but incomplete forBCK andBCI logic. We show thatD is complete for the relevance logic. One of the main steps is the proof of the formula ((a →a) →a) →a found in interaction with our resolution theorem prover. Various strategies of generating consequences of the axioms and choosing best ones for the next iteration were tried until the proof was found.

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Authors and Affiliations

  1. Institute of Cybernetics, Akadeemia tee 21, 200108, Tallinn, Estonia

    Grigori Mints & Tanel Tammet

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  1. Grigori Mints
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  2. Tanel Tammet
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Mints, G., Tammet, T. Condensed detachment is complete for relevance logic: A computer-aided proof. J Autom Reasoning 7, 587–596 (1991). https://doi.org/10.1007/BF01880330

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  • DOI: https://doi.org/10.1007/BF01880330

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