Abstract
The paper is concerned with the problem of characterization of strengthenings of the so-called Lukasiewicz-like sentential calculi. The calculi under consideration are determined byn-valued Lukasiewicz matrices (n>2,n finite) with superdesignated logical values. In general. Lukasiewicz-like sentential calculi are not implicative in the sense of [7]. Despite of this fact, in our considerations we use matrices analogous toS-algebras of Rasiowa. The main result of the paper says that the degree of maximality of anyn-valued Lukasiewicz-like sentential calculus is finite and equal to the degree of maximality of the correspondingn-valued Lukasiewicz calculus.
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References
R. S. Grigolia,Algebraic analysis of Lukasiewicz-Tarski's n-ralued logical calculi (in Russian),Proceedings of Tbilisi University. A 6–7, 149–150. Mathematical and Natural Sciences, Tbilisi (1973), pp. 121–132.
J. Lukasiewicz, A. Tarski,Untersuchungen über den Aussagenkalkül.Comptes-rendus des séances de la Société des Sciences et de Lettres de Varsorie, Cl. III. 23 (1930), pp. 30–50.
G. Malinowski,Matrix representation for the dual counterparts of Lukasiewicz n-ralued 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.
G. Malinowski,S-algebras for n-ralued sentential calculi of Lukasiewicz. The degrees of marimality of some Lukasicwicz's logics, in:Selected papers on Lukasiewicz sentential calculi. Ed. R. Wójcicki, ass. ed. G. Malinowski, Ossolineum, 1977, pp. 149–159.
P. Mangani,Su certe algebra conesse con logische a piú ralori,Bolletino della Unione Matematica Italiana, (4) 8 (1973), pp. 68–78.
R. McNaughton,A theorem about infinite-valued sentential logic,Journal of Symbolic Logic, 16 (1951), pp. 1–13.
H. Rasiowa,An algebraic approach to non classical logics, North Holland Publishing Company, Amsterdam, Polish Scientific Publishers, Warszawa, 1974.
A. Rose,The degree of completeness of the m-valued Lukasiewicz propositional calculus,The Journal of the London Mathematical Society. 27 (1952), pp. 92–102.
J. B. Rosser, A. R. Turquette,Many-valued logics, North-Holland Publishing Company. Amsterdam, 1952.
R. Wójcicki,The logics stronger than three-valued sentential calculus. The notion of degree of macimality rersus the notion of degree of completeness,Studia Logica, XXXIII (1974), No. 2. pp. 201–214.
R. Wójcicki,Matrir approach in methodology of sentential calculi.Studia Logica, XXXII (1973), pp. 7–37.
R. Wójcicki,On matrix representations of consequence operations of Łukasiewicz sentential calculi,Zeitschrift für mathematische Logil: und Grundlagen der Mathematik. 19 (1973), pp. 239–247.
R. Wójcicki,A theorem on the finiteness of the degree of marimality of the n-valued Lukasiewicz logics,Proceedings of the V-th International Symposium on Multiple-Valued Logics, Indiana University. Bloomington, May 1975, pp. 240–251.
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Allatum est die 15 Octobris 1976
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Malinowski, G. Degrees of maximality of Klukasiewicz-like sentential calculi. Stud Logica 36, 213–228 (1977). https://doi.org/10.1007/BF02121267
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DOI: https://doi.org/10.1007/BF02121267