Logike sa integralima u uslovnim očekivanjima

Abstract

It could say that the research of logical systems in the dissertation goes in two directions: the first one is related to probability theory i.e. measure theory, while the other direction is related to topology. The main subject of this dissertation is extending the classical logic to formal systems which will be adequate for describing and concluding in the mentioned mathematical environments. The first part represents follow-up of works by M. Rašković and R. Đorđević in the area of probability logics and especially in the area of biprobability logics. The focus is on the logics with integral operators and logics with conditional expectation operators. The topological class logic [11, 12], which is adequate for studying the notions of topological product and continuous functions on topological class-spaces, is presented in the second part of this dissertation.