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In the paper we make an attempt to reconstruct Nikolai Vasiliev's logical systems by means of modern symbolic logic. We put forward the formalization of Vasiliev's assertoric syllogistic with three initial types of categorical propositions and the Law of excluded fourth. We set up the axiomatic calculus and the adequate semantics for it in order to reconstruct the main version of Vasiliev's imaginary logic. Metatheoretic relations between Vasiliev's logic of n dimensions and n-valued predicate logic are established. We also make clear that Vasiliev has developed a sketch of original system of intensional logic (as an alternative version of imaginary logic). We offer the calculus and semantics for the explication of this idea. (The part of this paper was published earlier. In: Markin V.I. What Trends in Non-Classical Logic Were Anticipated by Nikolai Vasiliev? Logical Invest 19:122–135, 2013.)

DOI: 10.1007/978-3-319-66162-9_7

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