This volume opens with a paper by V.I. Markin, which constructs a theory for analyzing reasoning where premises and conclusions are existential judgments and their Boolean combinations. Weijun Shi proposes an innovative technique for proving completeness in normal modal logics. L.Yu. Devyatkin investigates the proof-theoretic properties of three-valued logics based on the expressive capabilities of their languages. Masoud Alvand's paper examines issues related to logical pluralism. E.N. Lisanyuk presents a methodology for logical-argumentative analysis of desire statements serving as premises in non-demonstrative practical arguments about actions. H.K. Kadyg-ool's paper attempts to provide a relatively comprehensive examination of the non-classical logic ideas of Scottish logician, mathematician, and philosopher Hugh MacColl (1837–1909).