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Russia Izhevsk
Section  Computer science 
Title  Propositional logic on the basis of algebraic system containing traditional syllogistics 
Author(s)  Smetanin Yu.M.^{a} 
Affiliations  Udmurt State University^{a} 
Abstract  The article explains the reasons to replace the multisemantic basis of Aristotle in classical logic and traditional syllogistic with a monosemantic basis, isomorphic to relationships ''equivalent", ''entailing", ''independent", which happen between terms of reasoning and random events in probability theory. Theoretical results and applications are discussed. The author identifies the drawbacks of the mathematical model which is the basis of classical logics. An advanced version of the mathematical model which is logic $\textbf{S}_{L_1}$, based on nondegenerative Boolean algebra and an adjoint algebraic setbased system, is proposed. The article considers a nonclassical interpretation of judgments in the orthogonal basis of syllogistics; it also describes the opportunities of effective computer validation of logical implication in semantics. A new method of solving logic equations is presented. The samples of solutions are presented. 
Keywords  syllogistics, orthogonal basis of syllogistics, Boolean algebra, calculations of constituent, homomorphism of algebraic systems, logical sequence in semantic sense, probability, logical equations 
UDC  510.63 
MSC  03A10, 03G05, 06E30 
DOI  10.20537/vm130213 
Received  11 December 2012 
Language  Russian 
Citation  Smetanin Yu.M. Propositional logic on the basis of algebraic system containing traditional syllogistics, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 2, pp. 127146. 
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