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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Autor principal: Cignoli, R.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: Kluwer Academic Publishers 1991
Acceso en línea:Registro en Scopus
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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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