Abstract
At the present time there is a considerable number of reports in the literature on the generation of machine programs realizing the deduction search in the propositional and predicate calculuses. The question of machine programs capable of generating “sufficiently interesting” theorems of some kind of axiomatically given theories is also discussed in the literature. The difficulty in this problem is the question of what theorems might naturally be considered “sufficiently interesting.” Some possible approaches to this theorem are considered in [1], [2], [3].
The main results of this note were presented to the Leningrad Seminar on Mathematical Logic on October 14, 1965.
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Literature Cited
Wang Hao, “Toward mechanical mathematics,” IBM J. Res. and Dev., 4(1): 2–22 (1960).
Glushkov, V. M., Introduction to Cybernetics, Kiev, 1964.
Glushkov, V. M., Cybernetics and Intellectual Labor, Moscow, 1965.
Davydov, G. V., “Method of establishing deducibility in classical predicate calculus,” this volume, p. 1.
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Daydov, G.V. (1969). On the Correction of Unprovable Formulas. In: Slisenko, A.O. (eds) Studies in Constructive Mathematics and Mathematical Logic. Seminars in Mathematics, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8968-2_2
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DOI: https://doi.org/10.1007/978-1-4684-8968-2_2
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