phone +7 (3412) 91 60 92

Archive of Issues


Russia Izhevsk
Year
2013
Issue
2
Pages
127-146
<<
Section Computer science
Title Propositional logic on the basis of algebraic system containing traditional syllogistics
Author(-s) Smetanin Yu.M.a
Affiliations Udmurt State Universitya
Abstract The article explains the reasons to replace the multi-semantic basis of Aristotle in classical logic and traditional syllogistic with a mono-semantic 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 non-degenerative Boolean algebra and an adjoint algebraic set-based system, is proposed. The article considers a non-classical 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. 127-146.
References
  1. Bocharov V.A., Markin V.I. Sillogisticheskie teorii (Syllogistic theories), Moscow: Progress–Traditsiya, 2010.
  2. Smetanin, Yu.M. Analysis of paradoxes of tangible implication in the orthogonal basis of syllogistics, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2011, no. 4, pp. 144–162.
  3. Smetanin Yu.M. Algorithm for solving polysyllogizm in the orthogonal basis by calculating the constituent sets, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2010, no. 4, pp. 172–185.
  4. Smetanin Yu.M., Smetanin M.Yu. Medical diagnostics and orthogonal basis of syllogistics, Proceedings of 2nd International Conference (OSTIS–2012), Minsk, 2012, pp. 289–296.
  5. Smetanin Yu.M. Probabilistic logics and orthogonal basis of syllogistics, Proceedings of 2nd International Conference (OSTIS–2012), Minsk, 2012, pp. 479–488.
  6. Smetanin Yu.M. Orthogonal logic-probable model for risk estimation in management, Vestn. Udmurt. Univ. Econ. Law, 2012, no. 3, pp. 66–73.
  7. Smetanin Yu.M. Formal logics on the orthogonal basis of syllogistics, Logics, Language and Formal Models: Transactions, St. Petersburg: St. Petersburg State University, 2012, pp. 131–144.
  8. Kulik B.A., Zuenko A.A., Fridman A.Ya. Algebraicheskii podkhod k intellektual’noi obrabotke dannykh i znanii (Algebraic approach to intellectual data and knowledge processing), Saint-Petersburg State Polytechnical University, 2010.
  9. Kulik B.A. Logicheskie osnovy zdravogo smysla (Logic basis of the common sense), St. Petersburg: Politekhnika, 1997.
  10. Vladimirov D.A. Bulevy algebry (Boolean algebras), Мoscow: Nauka, 1969.
  11. Zakrevskii A.D. Logicheskie uravneniya (Logical equations), Мoscow: Editorial URSS, 2003.
  12. Gorbatov V.A. Teoriya chastichno uporyadochennykh sistem (The theory of partially-ordered systems), Мoscow: Soviet radio, 1976.
  13. Kolmogorov A.N. Teoriya veroyatnostei i matematicheskaya statistika (Probability theory and mathematical statistics), Мoscow: Nauka, 1986.
  14. Ryabinin I.A. Logical probabilistic calculus as the tool of research reliability and safety of structurally-complicated systems, Аvtomatika i Тelemekhanika, 2003, no. 7, pp. 178–186.
  15. Solozhentsev E.D. Upravlenie riskom i effektivnost’yu v ekonomike: logiko-veroyatnostnyi podkhod (Risk and efficiency management in economics: logical probabilistic approach), St. Petersburg: St. Petersburg State University, 2009, 250 p.
  16. Russell S., Norvig P. Artificial intellect: modern approach. Second еdition, Williams Publishing House, 2006.
  17. Courant R., Robbins H. What is mathematics? An Elementary Approach to Ideas and Methods, London: Oxford University Press, 1996.
Full text
<< Previous article