In the monograph "The Philosophical Problems of Multivalued Logic" (1960), Zinoviev reviewed almost all multivalued logical systems, analyzed the place, main results and applicability of multivalued logic in the logic and methodology of science. In subsequent works, he developed his own concept of logic, which he called "complex logic". The problem of logic, according to Zinoviev, was not in formal mathematical calculus, but in the development of "methods of reasoning, proof, methods of scientific knowledge". Zinoviev tried, firstly, to overcome the classical and intuitionistic versions of logic and, secondly, to expand the field of logic research based on the methodology of empirical sciences. The subject of logic is language, it does not discover, but invents specific rules of language — logical rules — and introduces them into language practices as artificial means of systematization. This prescriptivist approach is close to the late Wittgenstein. Zinoviev insisted on the universality of logic, claiming the independence of logical rules from the empirical areas of their application. He denied ontological status to such concepts as a point or zero, considering them tools of knowledge; his approach in Western literature was characterized as logical nominalism. Zinoviev's pupil, the German logician Horst Wessel, noted that his logic was based on syntax, not semantics.