Czasopismo
2004
|
Vol. 37, nr 2
|
245--254
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
The cardinal of the finitely generated free (n + l)-valued Lukasiewicz BCK- algebras has been determined by different authors only for some values of n. In this article we find the formula that allows its calculus for every value of n. By the application of this formula for n = 1, n = 2, we corroborate the results obtained by L. Iturrioz and A. Monteiro (Rev. Un. Mat. Argentina, 22 (1966), 146) and L. Iturrioz and O.Rueda (Discrete Math., 18 (1977), 35-44). In addition we generalize the results found by A. V. Figallo (Rev. Un. Mat. Argentina, 41, 4 (2000), 33-43).
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
245--254
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- Departamento de Matemática, Universidad Nacional del Sur, 8000 Bahia Blanca, Argentina, adolf@criba.edu.ar
autor
- Departamento de Matemática, Universidad Nacional del Sur, 8000 Bahia Blanca, Argentina, martinf@criba.edu.ar
autor
- Departamento de Matemática, Universidad Nacional del Sur, 8000 Bahia Blanca, Argentina, aziliani@criba.edu.ar
Bibliografia
- [1] B. Bosbach, Residuation grupoids, Bull. Acad. Sci. Sr. Sci. Math. Astronom. Phys. 22 (1974), 103-104
- [2] C. C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490.
- [3] A. V. Figallo, In+1 - álgebras con operaciones adicionales, Doctoral Thesis, Univ. Nac. del Sur , 1989, Bahia Blanca, Argentina.
- [4] A. V . Figallo, Free (n+1) - valued C-algebras, Rev. Un. Mat. Argentina 41, 4 (2000), 33-43.
- [5] J. M. Font, A. Rodriguez and A. Torrens, Wajsberg algebras, Stochastica 8, 1 (1984), 5-31.
- [6] R. Grigolia, Algebraic analysis of Lukasiewicz-Tarski n-valued systems, in R. Wójcicki and G. Malinowski (Eds.) Selected Papers on Lukasiewicz Sentential Calculi, Ossolineum, Wroclaw and Warsaw (1977), 81-92.
- [7] Y. Imai and K. Iseki, On axiom systems of propositional calculi, Proc. Japan Acad. 42 (1966), 19-22.
- [8] K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebra, Math. Japonica 23 (1978), 1-26.
- [9] L. Iturrioz and A. Monteiro, Cálculo Proposicional implicativo clásico con n variables proposicionales, (Spanish) Rev. Un. Mat. Argentina 22 (1966), 146.
- [10] L. Iturrioz and O. Rueda, Algèbres implicatives trivalentes de Łukasiewicz libres, (French) Discrete Math. 18 (1977), 35-44.
- [11] Y. Komori, The separation theorem of the N₀-valued Łukasiewicz propositional logic, Rep. Fac. Sci., Shizuoka Univ. 12 (1978), 1-5.
- [12] R. Mc Naughton, A theorem about infinite - valued sentential logic, J. Symbolic Logic 16 (1951), 1-13.
- [13] R. K. Meyer, Pure denumerable Łukasiewiczian implication, J. Symbolic Logic 31 (1966), 575-580.
- [14] A. Monteiro, Algebras implicativas trivalentes de Łukasiewicz, Lectures given at the Univ. Nac. del Sur, Bahia Blanca, Argentina, 1968.
- [15] M. Pałasiński, Representation theorem for commutative BCK-algebras, Math. Sem. Notes Kobe Univ. 10 (1982), 473-478.
- [16] A. J. Rodriguez Salas, Un estudio algebraico de los cálculos proposicionales de Łukasiewicz, Doctoral Thesis, Univ. de Barcelona (1980).
- [17] A. Rose, Extensions de quelques theoremes de Me Naughton, C. R. Acad. Sci. Paris 292 (1981), 979-981.
- [18] S. Tanaka, On Λ-commutative algebras, Math. Sem. Notes Kobe Univ. 3 (1975), 59-64.
- [19] T. Traczyk, On the variety of bounded commutative BCK-algebras, Math. Japonica 24, 3 (1979), 283-292.
- [20] A. Wroński, On varieties of commutative BCK-algebras not generated by their finite members, Math. Japonica 30, 2 (1985), 227-233.
- [21] H. Yutani, Quasi-commutative BCK-algebras and conguence relations, Math. Sem. Notes Kobe Univ. 5 (1977), 469-480.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0010-0001