Analysis of paradoxes of tangible implication in the orthogonal basis of syllogistics
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2011), pp. 144-162

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The article analyzes the disadvantages of Aristotle syllogistic basis. The author indicates reasons for paradoxes of tangible implication in classical logics. It is suggested to verify correlations between a conditioned judgment and a tangible implication. Such paradoxes are not allowed in the multi-level syllogistic orthogonal basis.
Keywords: syllogistics, formal logics, orthogonal basis, Boolean algebra, multi-level syllogistics.
Mots-clés : paradoxes of tangible implication, polysyllogism
Yu. M. Smetanin. Analysis of paradoxes of tangible implication in the orthogonal basis of syllogistics. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2011), pp. 144-162. http://geodesic.mathdoc.fr/item/VUU_2011_4_a12/
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[1] Aristotel, Sochineniya v chetyrekh tomakh, v. 1, Mysl, M., 1975; т. 2, 1978

[2] Brusentsov N. P., Ustranenie paradoksov i khimer, Fond “Novoe tysyacheletie”, M., 2010

[3] Brusentsov N. P., Iskusstvo dostovernogo rassuzhdeniya. Neformalnaya rekonstruktsiya aristotelevoi sillogistiki i bulevoi matematiki mysli, Fond “Novoe tysyacheletie”, M., 1998

[4] Brusentsov N. P., Bluzhdanie v trekh sosnakh, Priklyucheniya dialektiki v informatike, SvR-Argus, M., 2000 URL: http://ternarycomp.narod.ru/3PINES.DOC

[5] Brusentsov N. P., “Logika i intellekt”, Iskusstvennyi intellekt, 2004, no. 2, 28–31

[6] Valkov K. I., Proektsionnoe modelirovanie i avtomatizatsiya, ucheb. posobie dlya fakulteta povysheniya kvalifikatsii, LISI, L., 1985, 86 pp.

[7] Vasilev N. I., Voobrazhaemaya logika. Izbrannye trudy, Nauka, M., 1989, 124 pp. | MR

[8] Vladimirov D. A., Bulevy algebry, Nauka, M., 1969, 264 pp. | MR

[9] Gilbert D., Akkerman V., Osnovy teoreticheskoi logiki, Inostr. lit., M., 1947

[10] Gorbatov V. A., Teoriya chactichno uporyadochennykh sistem, Sovetskoe radio, M., 1976, 336 pp. | MR | Zbl

[11] Zakrevskii D. A., “K formalizatsii polisillogistiki”, Logicheskii vyvod, Nauka, M., 1979, 300–309 | MR

[12] Kuzina E. B., Logika v kratkom izlozhenii i uprazhneniyakh, Izd-vo MGU, M., 2000, 240 pp.

[13] Kuzichev A. S., Diagrammy Venna, Nauka, M., 1968, 253 pp.

[14] Kulik B. A., Logicheskii analiz sistem na osnove algebraicheskogo podkhoda, dis. $\dots$ d-ra fiz.-matem. nauk, SPbGU, SPb., 2008, 266 pp. | MR

[15] Kulik B. A., Logicheskie osnovy zdravogo smysla, ed. D. A. Pospelov, Politekhnika, SPb., 1997, 131 pp.

[16] Kerrol L., “Simvolicheskaya logika”, Istoriya s uzelkami, Mir, M., 1973, 408 pp. | MR

[17] Lobanov V. I., Russkaya veroyatnostnaya logika, Russkaya pravda, M., 2009, 320 pp.

[18] Losev F. F., “Kriticheskie zametki o burzhuaznoi matematicheskoi logike”, Istoriko-matematicheskie issledovaniya. 2-ya seriya, 8(43), Yanus-K, M., 2003, 339–401 | MR

[19] Lukasevich Ya., Aristotelevskaya sillogistika s tochki zreniya sovremennoi formalnoi logiki, Inostr. lit., M., 1959

[20] Nefedov V. N., Osipova V. A., Kurs diskretnoi matematiki, Izd-vo MAI, M., 1992, 264 pp.

[21] Plutarkh, Sravnitelnye zhizneopisaniya v dvukh tomakh, v. 2, Nauka, M., 1994

[22] Poretskii P. S., O sposobakh resheniya logicheskikh ravenstv i ob obratnom sposobe matematicheskoi logiki, Kazan, 1884

[23] Rassel B., Iskusstvo myslit, Ideya-Press, Dom intellektualnoi knigi, M., 1999, 240 pp.

[24] Smetanin Yu. M., “Ortogonalnyi bazis sillogistiki ili kakaya logika nuzhna ekonomistam”, Menedzhment: teoriya i praktika (UdGU), 2009, no. 3–4, 25–42

[25] Smetanin Yu. M., “Sopostavlenie rasshirennoi algebry mnozhestv i algebry logiki s tochki zreniya problem polisillogistiki”, Menedzhment: teoriya i praktika (UdGU), 2010, no. 3–4, 12–27

[26] Smetanin Yu. M., “Ortogonalnyi bazis sillogistiki”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2009, no. 4, 155–166

[27] Smetanin Yu. M., “Algoritm resheniya polisillogizmov v ortogonalnom bazise posredstvom ischisleniya konstituentnykh mnozhestv”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2010, no. 4, 172–185