On the completeness of a~new intuitionistic connective
Matematičeskie zametki, Tome 60 (1996) no. 3, pp. 423-433.

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A. V. Bessonov suggested an example of an intuitionistic calculus that defines a new connective in the sense of P. S. Novikov. Using the Bessonov logic as an example, this definition is compared with a similar definition suggested by D. M. Gabbay to show that the Bessonov logic does not comply with Gabbay's definition. An example of a calculus that satisfies Novikov's definition but has no disjunctive property is constructed.
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A. D. Yashin. On the completeness of a~new intuitionistic connective. Matematičeskie zametki, Tome 60 (1996) no. 3, pp. 423-433. http://geodesic.mathdoc.fr/item/MZM_1996_60_3_a9/

[1] Dragalin A. G., Matematicheskii intuitsionizm. Vvedenie v teoriyu dokazatelstv, Nauka, M., 1979 | Zbl

[2] Smetanich Ya. S., “O polnote ischisleniya vyskazyvanii s dopolnitelnoi operatsiei ot odnoi peremennoi”, Tr. MMO, 9, URSS, M., 1960, 357–351

[3] Gabbay D. M., “On some new intuitionstic propositional connectives, 1”, Studia Logica, 36:1–2 (1977), 127–139 | DOI | MR | Zbl

[4] Bessonov A. V., “O novykh operatsiyakh v intuitsionistskom ischislenii”, Matem. zametki, 22:1 (1977), 23–28 | MR | Zbl

[5] Kirk R. E., “A characterisation of the classes of finite tree frames which are adequate for the intuitionistic logic”, Z. Math. Logik Grundlag. Math., 26:6 (1980), 497–501 | DOI | MR

[6] Yashin A. D., “Novaya intuitsionistskaya svyazka i uslovie edinstvennosti”, Tezisy Mezhrespubl. konf. po matem. logike, Kazan, 1992

[7] Skott D., “Sovety po modalnoi logike”, Semantika modalnykh i intensionalnykh logik, Progress, M., 1981, 280–317

[8] Sobolev S. K., “Ob intuitsionistskom ischislenii vyskazyvanii s kvantorami”, Matem. zametki, 22:1 (1977), 69–76 | MR | Zbl