# Method of Establishing Deducibility in Classical Predicate Calculus

## Abstract

In [1] and [2], S. Yu. Maslov proposed an “inverse method” of establishing deducibility in classical predicate calculus.^{†} In the deduction search by this method the “volume” of choices grows substantially as the quantity of favorable sets accumulated to a given time increases. Moreover, in discarding the ends of favorable sets by rule B in the “inverse method” some information is lost, whose utilization might shorten the subsequent process of establishing deducibility in a number of cases. Hence, it is expedient to try to decrease the quantity of objects participating in the choice by the maximal “merger” of favorable sets into one object (if only of more complex structure) and to take account of the mentioned information.

## Keywords

Inverse Method Trivial Extension Constructive Mathematic Logic Group Vertical Stroke## Preview

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## Literature Cited

- 1.Maslov, S. Yu., “Inverse method of establishing deducibility in classical predicate calculus,” Doklady Akad. Nauk SSSR, 159(1): 17–20 (1964).Google Scholar
- 2.Maslov, S. Yu., “Inverse method of establishing deducibility for vox prenex formulas of predicate calculus,” Doklady Akad. Nauk SSSR, 17(1): 22–25 (1967); Sov. Mat. 8 (1): 16–19 (1967).Google Scholar
- 3.Davydov, G. V., “On some approaches to machine production of new theorems,” II Symp. on Cybernetics (in Russian) (Abstracts), Tbilisi, 1965, p. 180.Google Scholar
- 4.Herbrand, J., Recherche sur la Théorie de la Demonstration, Warsaw, 1930.Google Scholar