Quasi-functionality in logic and other sciences

The paper reviews the author’s research on the problem of applying the methodological principle of quasi-functionality in logic and other areas of knowledge. The methodological principle of quasi-functionality lies in the interpretation of logical terms as quasi-functions, as well as in understanding the relationships between natural phenomena, social life and cognition as quasi-functional. Functionality is asserted to be a special case of quasi-functionality. It follows that determinism is a special case of quasi-determinism. The study describes the logical systems — calculus and their semantics — constructed by the author. Examples of the application of this principle in mathematics, humanitarian and natural sciences are given.

References
[1] Ivlev Yu.V. Logika norm. Diss. … kand. filos. nauk [Logic of norms. Cand. philos. sc. diss.]. Moscow, 1972, 180 p.
[2] Rescher N. Many-valued logic. New York, McGraw Hill, 1969, 359 р.
[3] Ivlev Yu.V. Kvazimatrichnaya (kvazifunktsionalnaya) logika [Quasi-matrix (quasi-functional) logic]. Moscow, Moscow University Press, 2018, 128 p.
[4] Ivlev Yu.V. Modalnaya logika [Modal logic]. Moscow, Moscow University Press, 1991, 224 p.
[5] Ivlev Yu.V. Soderzhatelnaya semantika modalnoy logiki [Meaningful semantics of modal logic]. Moscow, Moscow University Press, 1985, 170 p.
[6] Ivlev Yu.V. A semantics for modal calculi. Bulletin of the section of logic, 1988, vol. 17, no. 3–4, рр. 114–126.
[7] Ivlev Yu.V. Quasi-matrix logic. Journal of Multiple-Valued Logic and Soft Computing, 2005, vol. 11, no. 3–4, рр. 239–252.
[8] Ivlev Yu.V. Vestnik Moskovskogo universiteta. Ser. 7: Filosofiya — Moscow University Bulletin. Series 7. Philosophy, 1982, no. 5, pp. 57–68.
[9] Ivlev Yu.V. Soderzhatelnaya semantika modalnoy logiki [Meaningful semantics of modal logic]. In: Logiko-metodologicheskie issledovaniya [Logical and methodological studies]. Moscow, Moscow University Press, 1980, pp. 356–374.
[10] Ivlev Yu.V. Vestnik Moskovskogo universiteta. Ser. 7: Filosofiya — Moscow University Bulletin. Series 7. Philosophy, 1973, no. 6, pp. 61–70.
[11] Ivlev V.Yu. Filosofiya i obshchestvo — Philosophy and Society, 1977, no. 3, pp. 108–125.
[12] Ivlev V.Yu., Ivlev Yu.V. Logicheskie issledovaniya — Logical investigations, 2018, vol. 24, no. 2, pp. 92–99.
[13] Coniglio M.E., Golzio A.C. Swap structures semantics for Ivlev-like model logics. International Journal of Soft Computing, 2019, vol. 23, no. 7, pp. 2243–2254.
[14] Coniglio M.E., del Cerro L.F., Peron N.M. Finite non-deterministic semantics for some model systems. Journal of non-Classical Logics, 2015, vol. 25, no. 1, рр. 20–45.
[15] Omori H., Skurt D. More Modal Semantics Without Possible Worlds. IFColog Journal of Logics and their Applications, 2016, vol. 3, рр. 815–846.