We continue our investigation of the proof searching procedures developed for natural deduction calculus for classical and a variety of non-classical logics. In particular, we deal with natural deduction systems for propositional logics I⟨alpha;beta⟩, where alpha, beta are elements of 0, 1, 2, 3,..., w such that I⟨0;0⟩ is classical logic, proposed by Vladimir Popov. We aim at generalising the concept of an inference for these systems that is fundamental to proof searching technique for these logics.
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