A method for random sampling of well-formed formulas. (A method for random sampling of formulas of an elementary theory and statistical estimation of their deducibility equipped by a program. I.)

This paper represents a rather shortened version of the first part of a report the title of which can be found in the parentheses following the title of this paper. It deals with a method which enables to realize a random sampling of well-formed formulas of an appropriate formalized theory by using random numbers. Some possibilities of application of this method are mentioned in the closing section. First an appropriate formulation for the first-order functional calculus is described in this paper. This formulation arises when Gentzen's sequences calculus, Church's Pj-calculus and Ohama's calculus are combined together (as to Ohama's calculus see [1]). Then a procedure is constructed, transforming any sequence of indices (including random ones) into a well-formed formula of a formerly given theory based on the above formulated first-order calculus. In the theorems 1 — 3 some principal properties of this procedure are described. Questions which arise in connection with methods for a further investigation of the formulas we have obtained are not investigated in this paper and will be left for the following one. The suggested program, describing the above mentioned procedure in FORTRAN and based on the method of so-called pseudorandom numbers, which is enclosed to the report mentioned above is not enclosed to this paper because of its extent.