Abstract
A formal language whose propositions express (in some sense) the properties of propositional formulas is described in the paper. For a certain subset of propositions of this language it is proved that each of them defines a class of propositional formulas, on which it is possible to recognize the tautological nature in a time polynomially dependent on the formula's length.
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Literature cited
D. Prawitz, “Advances and problems in mechanical proof procedures,” Machine Intelligence, No. 4, 59–71 (1969).
G. V. Davydov and P. Yu. Suvorov, “Reduction of propositional tautology to graph coloring in three colors,” Zap. Nauch. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,40, 10–13 (1974).
E. Mendelson, Introduction to Mathematical Logic, Van Nonstrand and Reinhold Co., New York (1979).
Additional information
Translated fromZapiski Nauchnykh Seminarov Leningradskogo Matematicheskogo, Otdeleniyaim. V. A.Steklova Akad.Nauk SSSR, Vol. 60, pp. 197–206,1976. Result announced December 4, 1974.
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Suvorov, P.Y. On the recognition of the tautological nature of propositional formulas. J Math Sci 14, 1556–1562 (1980). https://doi.org/10.1007/BF01693987
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DOI: https://doi.org/10.1007/BF01693987