Truth values of quasi-functional logic: generalized historical review
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04.07.2026
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Abstract
The article is concerned with the historical analysis of special truth values forming within the development of quasi-functional logic. Thus, it implies the review of the works of Hans Reichenbach, Zygmunt Zawirsky, Nicholas Rescher, Yuriy Vasilievich Ivlev and those of some others. Reichenbach’s background was a probabilistic approach and many-valued logic. Truth values were interpreted in a probabilistic way, later new implication was presented quasi-implication, which definition needed third truth value — “indetermined”. Zawirsky proposed an approach within two classic logic values – 1 and 0, actually defining special truth value “1 or 0”. Later N. Rescher, Yu.V. Ivlev, J. Kearns independently formulated various quasi-functional logics, all of them were concerned with an analysis of an important role of the propositions’ truth. Relevant ideas of L. Wittgenstein and L. Goddard are also reviewed. Beyond the results of the analysis of the presented theme, some questions for further research are being formulated in the conclusion.
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How to Cite
Kadyg-ool K. K. Truth values of quasi-functional logic: generalized historical review // Logicheskie Issledovaniya / Logical Investigations. 2026. VOL. 32. № 1. C. 80-96.
Issue
Section
Non-classical logics
Copyright (c) 2026 Хулербен Кок-оолович Кадыг-оол
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
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Sylvan R. Significant moments in the development of Australian logic: in critical appreciation of Leonard Goddard's major contribution // Logique et Analyse. 1992. Vol. 35. No. 137/138. P. 5-44.
Szumilewicz-Lachman I. Zygmunt Zawirski: his life and work. With Selected Writings on Time, Logic and The Methodology of Science. Dordrecht: Springer Science+Business Media, 1994. 383 p.
Wittgenstein L. Some Remarks on Logical Form // Proceedings of the Aristotelian Society, Supplementary Volumes. 1929. Vol. 9, Knowledge, Experience and Realism. P. 162-171.
Zawirsky Z. Les rapports de la logique polyvalente avec le calcul des probabilités // Actes du Congrès international de philosophie scientifique, Sorbonne, Paris, 1935: IV. Induction et probabilité. Paris: Hermann et cie, 1936. P. 40-45.
Ивлев Ю.В. Модальная логика. М.: Изд. МГУ, 1991. 221 с.
Ивлев Ю.В. Квазиматричная логика – основа теории фактических (физических) модальностей // Логические исследования: ежегодник. 2001. № 9. С. 103-113.
Ивлев Ю.В. Квазиматричная (квазифункциональная) логика. М.: Изд. МГУ, 2018. 191 с.
Ивлев Ю.В. Квазифункциональные отношения в логике и других областях знания // Вестник Томского государственного университета. Философия. Социология. Политология. 2021. №63. С. 214-235.
Кадыг-оол Х.К. Истоки квазиматричной логики // Известия Академии наук Республики Таджикистан. Отделение общественных наук. 2013. №2. С. 71-74.
Кадыг-оол Х.К. Матричные и кввазиматричные системы алетической модальной логики. Кызыл: Тип. Аныяк, 2017. 100 с.
Трулстра А.С. Введение // Справочная книга по математической логике. Ч. IV. Теория доказательств и конструктивная математика. М.: Наука, 1983. С. 7-8.
Avron A., Zamansky A. Non-deterministic semantics for logical systems // Handbook of philosophical logic. Vol. 16 / Ed. by D.M. Gabbay, F. Guenthner. Dordrecht, Heidelgerg, London, New-York: Springer, 2011. P. 227-304.
Coniglio M., Da Cruz Silvestrini L.H. An alternative approach for quasi-truth // Logic Journal of IGPL. 2014. Vol. 22. No. 22. P. 387-410.
da Costa N.C.A., Alves E.H. A semantical analysis of the calculi Cn // Notre Dame Journal of Formal Logic. 1977. Vol. 18. No. 4. P. 621-630.
Eberhardt F., Glymour C. Hans Reichenbach’s probability logic // Handbook of the History of Logic. Volume 10: Inductive Logic / Ed. by S. Hartmann, D.M. Gabbay, J. Woods. Amsterdam: Elsevier, 2011. P. 357-388.
Goddard L. The exclusive 'Or' // Analysis. 1960. Vol. 20. No. 5. P. 97-105.
Grigoryev O., Petrukhin Ya. Non-deterministic Logic of Generalized Classical Truth Values // Many-valued semantics and modal logics: essays in honour of Yuriy Vasilievich Ivlev / Ed. by M.E. Coniglio, E. Kubyshkina, D. Zaitsev. Studies in Epistemology, Logic, Methodology, and Philosophy of Science. Vol. 485. Cham: Springer, 2024. P. 93-109.
Kearns J.T. Modal semantics without possible worlds // Journal of Symbolic Logic. 1981. Vol. 46. No. 1. P. 77-86.
Many-valued semantics and modal logics: essays in honour of Yuriy Vasilievich Ivlev // Studies in Epistemology, Logic, Methodology, and Philosophy of Science. Vol. 485 / Ed. by M.E. Coniglio, E. Kubyshkina, D. Zaitsev. Cham: Springer, 2024. 323 p.
Omori H., Skurt D. More modal semantics without possible worlds // IfCoLog Journal of Logics and Their Applications. 2016. Vol 3. No. 5. P. 815-846.
Reichenbach H. Sur les fondements logiques de la probabilité // Recherches philosophiques. 1934. No. 4. P. 361-370.
Reichenbach H. Die bedeutung des wahrsch ei nlichkeitsbegriffes für die erkenntnis // Actes du huitième Congrès International de Philosophie. à Prague, 2-7 septembre 1934. Prague, 1936. P. 163-169.
Reichenbach H. Les fondements logiques du calcul des probabilités // Annales de l’I. H. P. 1937. Tome 7. No. 5. P. 267-348.
Reichenbach H. Philosophic Foundations of Quantum Mechanics. Berkeley and Los Angeles: Univ. of California Press, 1944. 182 p.
Rescher N. Quasi-Truth-Functional Systems of Propositional Logic / The Journal of Symbolic Logic. 1962. Vol. 27. No. 1. P. 1-10.
Rescher N. Many-valued logic. New York: McGraw-Hill Book Company, 1969. 288 p.
Sylvan R. Significant moments in the development of Australian logic: in critical appreciation of Leonard Goddard's major contribution // Logique et Analyse. 1992. Vol. 35. No. 137/138. P. 5-44.
Szumilewicz-Lachman I. Zygmunt Zawirski: his life and work. With Selected Writings on Time, Logic and The Methodology of Science. Dordrecht: Springer Science+Business Media, 1994. 383 p.
Wittgenstein L. Some Remarks on Logical Form // Proceedings of the Aristotelian Society, Supplementary Volumes. 1929. Vol. 9, Knowledge, Experience and Realism. P. 162-171.
Zawirsky Z. Les rapports de la logique polyvalente avec le calcul des probabilités // Actes du Congrès international de philosophie scientifique, Sorbonne, Paris, 1935: IV. Induction et probabilité. Paris: Hermann et cie, 1936. P. 40-45.