The problem of degrees of maximality. (A survey)

Autor

  • Grzegorz Malinowski Chair of Logic and Methodology of Sciences, University of Lodz image/svg+xml

DOI:

https://doi.org/10.18778/0208-6107.03.04

Abstrakt

Artykuł jest celnym przeglądem metod dowodzenia twierdzeń o stopniach maksymalności i rezultatów uzyskanych w tej dziedzinie do 1979 r .

Bibliografia

Anderson J. G., The degree of completeness of Dummet LC and Thomas LCn, "The Journal of the London Mathematical Society", 3(1971), pp. 558-569.
Google Scholar DOI: https://doi.org/10.1112/jlms/s2-3.3.558

Dzik W., Wroński A., Structural completeness of Gödel’s and Dummet’s propositional calculi, “Studia Logica", 32(1973), pp. 69-73.
Google Scholar DOI: https://doi.org/10.1007/BF02123815

Grigolia R. S. , Algebraic analysis of Lukasiewicz-Tarski’s n-valued logical calculi ( in Russian), "Proceedings of Tbilisi University ", A 6-7, 149-150. Tbilisi 1973, pp. 121-132.
Google Scholar

Łoś J., Suszko R., Remarks on sentential logics, "Indagationes Kathematicae", 20 (1958), pp. 177-103.
Google Scholar DOI: https://doi.org/10.1016/S1385-7258(58)50024-9

Łukasiewicz J., Tarski A., Untersuchungen über den Aussagenkalkul, "Comptes-rendus des séances de la Societé des Sciences et de Lettres de Varsovie", Cl. III, 23 (1930), pp. 30-50.
Google Scholar

Maduch H., On Lindenbaum’s algebras of finite implicational Łukasiewicz logics, "Bulletin of the Section of Logic ", 5(1976), No 1, pp. 29-32.
Google Scholar

Makinson D., A characterization of structural completeness of a structural consequence operations, "Reports on Mathematical Logic", 6(1976), No 4, pp. 99-102.
Google Scholar

Malinowski G., Degrees of maximality of Łukasiewicz - like sentential calculi, "Studia Logica", 36(1977), No 3, pp. 213-228.
Google Scholar DOI: https://doi.org/10.1007/BF02121267

Malinowski G., Matrix representations for the dual counterparts of Łukasiewicz n-valued sentential calculi and the problem of their degrees of maximality, "Proceedings of the V-th International Symposium on Multiple-Valued Logics". Indiana University , Bloomington, May 1975, pp. 252-261.
Google Scholar

Malinowski G., S-algebras and the degrees of maximality of three and four valued logics of Łukasiewicz, "Studia Logica” 33(1974), No 4, pp. 201-213.
Google Scholar DOI: https://doi.org/10.1007/BF02123377

Malinowski G., S-algebras for n-valued sentential calculi of Łukasiewicz. The degrees o f maximality of some Łukasiewicz’s logics, [in:] Selected papers on Łukasiewicz sentential calculi, Ed. R. Wójcicki, G. Malinowski, Ossolineum 1977, pp. 149-159.
Google Scholar

Malinowski G. , Spasowski M., Dual counterparts of Łukasiewicz’s sentential calculi, "Studia Logica", 33(1974), No 2, pp. 153-162.
Google Scholar DOI: https://doi.org/10.1007/BF02120491

Moisil Gr. C ., Essais sur les logiques non chrysippiennes, Editions de l’Académie de la Republique Socialiste de Roumania, Bucarest 1972.
Google Scholar

McNaughton, A theorem about infinite-valued sentential logic , "Journal of Symbolic Logic", 16(1951), pp. 1-13.
Google Scholar DOI: https://doi.org/10.2307/2268660

Pogorzelski W. A., Structural completeness of the prepositional calculus, "Bulletin de l'Academié Polonaise des Sciences", Série de mathematiques, astronomiques et physiques , 19(1971), No 5, pp. 349-351.
Google Scholar

Prucnal T., Proof of structural completeness of a certain class of implicative prepositional calculi, "Studia Logica", 32(1973), pp. 93-98.
Google Scholar DOI: https://doi.org/10.1007/BF02123821

Rasiowa H., An algebraic approach to non-classical logics, North Holland Publishing Company, Amsterdam, Polish Scientific Publishers, Warszawa 1974.
Google Scholar

Tarski A., Fundamentale Begriffe der Methodologie der deduktiven Wissenschaften, “Monatshefte für Mathematik und Physik", 37(1930), pp. 361-404.
Google Scholar DOI: https://doi.org/10.1007/BF01696782

Tokarz M., Connections between some notions of completeness of structural prepositional calculi, "Studia Logica", 32(1973), pp. 77-89.
Google Scholar DOI: https://doi.org/10.1007/BF02123818

Tokarz M., Degrees of maximality of three- and four-valued-RM-extensions, "Reports on Mathematical Logic", 9(1977), pp. 63-69.
Google Scholar

Tokarz M., Maximality, post-completeness and structural completeness, "Technical Report", No 2 / sf, Institute of Philosophy and Sociology, Polish Academy of Sciences, Wrocław, February 1978.
Google Scholar

Tokarz M., A remark on maximal matrix consequences, "Bulletin of the Section of Logic", 6(1977), No 4 , pp. 150-192.
Google Scholar

Tokarz M., A strongly finite logic with infinite degree of maximality, "Studia Logica", 35(1976), No 4 , pp. 447-451.
Google Scholar DOI: https://doi.org/10.1007/BF02123409

Wojtуlak P. , On structural completeness o f many-valued logics , "Studia Logica", 37(1978), No 2, pp. 139-147.
Google Scholar DOI: https://doi.org/10.1007/BF02124799

Wójcicki R „ The degree o f completeness of the finite-valued prepositional calculi, Zeszyty Naukowe U.J., Prace z Logiki, z. 7 , Kraków 1972, pp. 77-85.
Google Scholar

Wójcicki R., Dual counterparts of consequence operations, "Bulletin of the Section of Logic", 2(1973), No 1, pp. 55-57.
Google Scholar

Wójcicki R., The logics stronger than three-valued sentential calculus. The notion of degree of maximality versus the notion of degree of completeness, "Studia Logica", 33(1974), No 2 , pp. 201-214.4
Google Scholar DOI: https://doi.org/10.1007/BF02120495

Wójcicki R., Matrix approach in methodology of sentential calculi, "Studia Logica", 32 (1973), pp. 7-37.
Google Scholar DOI: https://doi.org/10.1007/BF02123806

Wójcicki R., Some remarks on the consequence operations in sentential logics, "Fundamenta Mathematicae", 58(1970), pp. 269-279.
Google Scholar DOI: https://doi.org/10.4064/fm-68-3-269-279

Wójcicki R., Strongly finite sentential calculi, [in:] Selected papers of Łukasiewicz sentential calculi, Ed. R. Wójcicki , G. Malinowski, Ossolineum 1977, pp. 53-77.
Google Scholar

Wójcicki R ., A theorem on the finiteness of the degree of maximality of the n-value Łukasiewicz logics,"Proceedings of the V-th international Symposium on Multiple-Valued Logica", Indiana University , Bloomington, May 1975, pp. 240-251.
Google Scholar

Wroński A., On finitely based consequence operations, "Studia Logica", 35(1976), No 4, pp. 453-458.
Google Scholar DOI: https://doi.org/10.1007/BF02123410

Opublikowane

1985-01-01

Jak cytować

Malinowski, G. (1985). The problem of degrees of maximality. (A survey). Acta Universitatis Lodziensis. Folia Philosophica. Ethica-Aesthetica-Practica, (3), 37–57. https://doi.org/10.18778/0208-6107.03.04

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