Approaches to the semantic definition of logical implication relation

The article considers two types of definition of the fundamental concept of logic, i.e. the logical implication relation. The first type is associated with the tradition of defining logical implication through the requirements for the inheritance of values. The variability of this approach involves different possibilities of setting a variety of assessments. The second type of definition is related to the computational consecution model.

References
[1] Vasilyev N.N. Logika i metalogika [Logic and meta-logic]. Moscow, Logos Publ., 1912, pp. 50-63.
[2] Belnap N.D. How a computer should think. In: Ryle G., ed. Contemporary Aspects of Philosophy. Stocksfield, Oriel Press Ltd. Publ., 1977, pp. 30-55 [In Russ.: Belnap N. Kak nuzhno rassuzhdat kompyuteru. In: Belnap N., Steel T. Logika voprosov i otvetov. Moscow, Progress Publ, 1981, 290 p.].
[3] Segerberg K. Theoria, 1967, vol. 33, pp. 53-71.
[4] Dunn J.M. A Comparative study of various model-theoretic treatments of negation: a history of formal negation. In: Gabbay D. M., Wansing H., eds., What is Negation? Applied Logic Series, 13, Kluwer Academic Publ., Dordrecht, 1997, 600 p.
[5] Voishvillo E.K. Simvolicheskaya logika (klassicheskaya i relevantnaya). Filosofsko-metodologicheskie aspekty [Symbolic logic. Classical and relevant. Philosophical and methodological aspects]. Moscow, Librokom Publ., 2011, 152 p.
[6] Smirnova E.D. Logicheskaya semantica i filosofskie osnovaniya logiki [Logical semantics and philosophical bases of logic]. Moscow, MGU Publ., 1986, 160 p.
[7] Hosli B., Jager G. Journal of Symbolic Logic, 1994, vol. 59, no. 2. pp. 473-485.
[8] Shalak V.I. Logicheskiye issledovaniya - Logical Investigations, 2006, iss. 13, pp. 273-285.
[9] Shalak V.I. Logicheskiye issledovaniya - Logical Investigations, 2006, iss. 13, pp. 286-302.
[10] Shramko Y., Wansing H. Journal of Philosophical Logic, 2005, vol. 34. pp. 121-153.
[11] Shramko Y. Die logische Wahrheitswerteontologie. In: Was folgt. Themen zu Wessel ente. Christiansen B., Scheffler U., eds. Berlin, Logos-Verlag, 2004. S. 149-169.
[12] Shramko Y., Dunn J.M., Takenaka T. Journal of Logic and Computation, 2001, vol. 11, pp. 761-788.
[13] Wansing H. Journal of Logic and Computation, 2001, vol. 11, pp. 759-760.
[14] Shramko Y., Wansing H. Studia Logica, 2009, vol. 91, no. 3, 160 p.
[15] Shramko Y., Wansing H. Studia Logica, 2009, vol. 92, no. 2, 137 p.
[16] Nevdobenko O.I. Otnoshenie sledovaniya i nestandartnye semantiki. Diss. cand. filos. nauk. Avtoreferat [The consecution relation and non-standard semantics. Cand. phylos. sc. diss. Author’s abstract]. Moscow, MGU Publ., 2000, 20 p.
[17] Finn V.K. Logicheskiye issledovaniya - Logical Investigations, 2006, iss. 13, pp. 155-189.