Sequent Axiomatization and Semantics of I-logics of Vasiliev’s Type

Abstract

I study here logics of Vasiliev‘s type were found in the process of explication of some of the ideas of the Russian logician and philosopher Nikolai Alexandrovich Vasiliev underlying his “imaginary logic”. This article demonstrates how to construct a simple and convenient search for proof of sequent axiomatization of $I$-logics of Vasiliev‘s type and how to build intuitively clear two-valued semantics, adequate $I$-logics of Vasiliev‘s type. In the present paper are defined by $I$-logics of Vasiliev‘s type, built their sequent axiomatization, provides the necessary semantic definitions and prove a theorem about the justification of $HI_{\langle\alpha,\beta\rangle}$-proofs (theorem 5) and theorem about the completeness of $HI_{\langle\alpha,\beta\rangle}$-proofs (theorem 6). The work concludes with a number of corollaries of these theorems and the announcement of a solution to the problem of existence of finite characteristic matrix for the logics of Vasiliev‘s type.