ИСТИНА

A. Arruda presented calculi to be formalizations of some ideas of N.A. Vasiliev. Calculus V1 is one of the calculi in question. Vasiliev fragment of the logic definable with A. Arruda’s calculus V1 (that is, a set of all V1-provable formulas each of which is as follows: each propositional variable occurring in the formula is a Vasiliev propositional variable) is of much interest. It should be noted the fragment in question is equal to the logic definable with calculus K1 presented by A. Sette. In the paper, (a) we define logics I1,1, I1,2, I1,3, …, I1,, which form (in the order indicated above) a strictly decreasing (in terms of the set-theoretic inclusion) sequence of sublogics in Vasiliev fragment of the logic definable with A. Arruda’s calculus V1.