The issue presents papers related to the fields of symbolic, non-classical and philosophical logic. The paper by M.N. Rybakov is devoted to the discussion of the conditions of Craig's theorem for theories having recursively enumerable and recursive axiomatizations. L.Yu. Devyatkin investigates all possible extensions of the well-known three-valued Kleene's logic and proves a number of important theorems. N.E. Tomova considers questions related to the definition of paracomplete logics, as well as questions of modal interpretation of paracomplete negation. The work of A.A. Pechenkin is devoted to the issues of various options for axiomatization of quantum logic. Another axiomatization, but this time of computational quantum logic, is constructed by V.L. Vasyukov. Syntax and semantics of non-hybrid first-order modal logic for cross-world predication is proposed by B.V. Borisov. The paper by V.I. Shalack is devoted to the analysis of the Turing model of computability and its natural generalization, in which Turing-incomputable functions are computable.