Zinoviev investigated a number of questions of non-classical logic, from the general theory of signs to a logical analysis of motion, causality, space and time. In "The Philosophical Problems of Multivalued Logic", multivalued logic was viewed as a generalization, not an abolition of classical two-valued logic, although Zinoviev concluded that the emergence of multivalued logic "dealt a blow" to the a priori classical logic. Later, Zinoviev developed a general theory of succession (the theory of inference), which was significantly different from classical and intuitionistic mathematical logic. According to Wessel, its originality was the introduction of the two-place predicate "from... logically follows..." into the formula for logical following, in fact, metatermine. The theory of logical calculus and the remaining sections of logic (the theory of quantifiers and predication, the logic of classes, normative and epistemic logic) were built on the basis of the theory. The work "Complex Logic" (1970) presented a systematic consideration of the formal apparatus for analyzing concepts, statements and evidence; a strict quantifier theory was formulated in the monograph that corresponded to intuitive assumptions; the properties of quantifiers were investigated.