Complete and atomic algebras of the infinite valued Łukasiewicz logic
The infinite-valued logic of Łukasiewicz was originally defined by means of an infinite-valued matrix. Łukasiewicz took special forms of negation and implication as basic connectives and proposed an axiom system that he conjectured would be sufficient to derive the valid formulas of the logic; this...
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
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Kluwer Academic Publishers
1991
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| LEADER | 05071caa a22005057a 4500 | ||
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| 003 | AR-BaUEN | ||
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| 008 | 190411s1991 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-0001160615 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Cignoli, R. | |
| 245 | 1 | 0 | |a Complete and atomic algebras of the infinite valued Łukasiewicz logic |
| 260 | |b Kluwer Academic Publishers |c 1991 | ||
| 270 | 1 | 0 | |m Cignoli, R.; Departamento de Matemática facultad de ciencias exactas y naturales, Ciudad Universitaria, Buenos Aires, 1428, Argentina |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Belluce, L.P., Semisimple algebras of infinite valued logic (1986) Canadian Journal of Mathematics, 38, pp. 1356-1379 | ||
| 504 | |a Birkhoff, G., (1967) Lattice Theory, , 3rd. edition, American Mathematical Society, Providence, R. L | ||
| 504 | |a Chang, C.C., Algebraic analysis of many-valued logics (1958) Transactions of the American Mathematical Society, 88, pp. 467-490 | ||
| 504 | |a Chang, C.C., A new proof of the completeness of the Łukasiewicz axioms (1959) Transactions of the American Mathematical Society, 93, pp. 74-80 | ||
| 504 | |a Font, J.M., Rodriguez, A.J., Torrens, A., Wajsberg algebras (1984) Stochastica, 8, pp. 5-31 | ||
| 504 | |a Iseki, K., Tanaka, S., An introduction to the theory of BCK-algebras (1978) Mathematica Japonica, 23, pp. 1-26 | ||
| 504 | |a Komori, Y., The separation theorem of the ℵ<inf>0</inf>-valued Łukasiewicz propositional logic (1978) Reports of the Faculty of Sciences, Shizuoka University, 12, pp. 1-5 | ||
| 504 | |a Komori, Y., Super Łukasiewicz propositional logics (1981) Nagoya Mathematical Journal, 84, pp. 119-133 | ||
| 504 | |a Lacava, F., Alcune proprietá delle Ł-algebre e delle Ł-algebre esistenzialmente chiuse (1979) Bolletino Unione Matemtica Italiana A(5), 16, pp. 360-366 | ||
| 504 | |a Mangani, P., Su certe algebre connesse con logiche a piú valori (1973) Bolletino Unione Matematica Italiana (4), 8, pp. 68-78 | ||
| 504 | |a Monteiro, A., Sur les algèbres de Heyting simétriques (1984) Portugalia Mathematica, 39, pp. 1-237 | ||
| 504 | |a Mundici, D., Interpretation of AFC*-algebras in Łukasiewicz sentential calculus (1985) Journal of Functional Analysis, 65, pp. 15-63 | ||
| 504 | |a Mundici, D., MV-algebras are categorically equivalent to bounded commutative BCK-algebras (1986) Mathematica Japonica, 31, pp. 889-894 | ||
| 504 | |a A. J. Rodríguez, Un estudio algebraico de los cálculos proposicionales de Łukasiewicz, Tesis Doctoral, Universidad de Barcelona, 1980; Romanowska, A., Traczyk, T., On commutative BCK-algebras (1980) Mathematica Japonica, 25, pp. 567-583 | ||
| 504 | |a Romanowska, A., Traczyk, T., Commutative BCK-algebras. Subdirectly irreducible algebras and varieties (1982) Mathematica Japonica, 27, pp. 35-48 | ||
| 504 | |a Tarski, A., (1950) Logic, Semantics, Metamathematics, , Clarendon Press, Oxford | ||
| 504 | |a Torrens, A., W-algebras which are Boolean products of members ofSR[1] and CW-algebras (1987) Studia Logica, 46, pp. 263-272 | ||
| 504 | |a Torrens, A., Boolean products of CW-algebras and pseudo-commplementation (1989) Reports on Mathematical Logic, 23, pp. 31-38 | ||
| 504 | |a Traczyk, T., On the variety of bounded commutative BCK-algebras (1979) Mathematica Japonica, 24, pp. 238-292 | ||
| 520 | 3 | |a The infinite-valued logic of Łukasiewicz was originally defined by means of an infinite-valued matrix. Łukasiewicz took special forms of negation and implication as basic connectives and proposed an axiom system that he conjectured would be sufficient to derive the valid formulas of the logic; this was eventually verified by M. Wajsberg. The algebraic counterparts of this logic have become know as Wajsberg algebras. In this paper we show that a Wajsberg algebra is complete and atomic (as a lattice) if and only if it is a direct product of finite Wajsberg chains. The classical characterization of complete and atomic Boolean algebras as fields of sets is a particular case of this result. © 1991 Polish Academy of Sciences. |l eng | |
| 593 | |a Departamento de Matemática facultad de ciencias exactas y naturales, Ciudad Universitaria, Buenos Aires, 1428, Argentina | ||
| 773 | 0 | |d Kluwer Academic Publishers, 1991 |g v. 50 |h pp. 375-384 |k n. 3-4 |p Stud Logica |x 00393215 |w (AR-BaUEN)CENRE-365 |t Studia Logica | |
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| 856 | 4 | 0 | |u https://doi.org/10.1007/BF00370678 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00393215_v50_n3-4_p375_Cignoli |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v50_n3-4_p375_Cignoli |y Registro en la Biblioteca Digital |
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