On axioms and some properties of monadic four-valued modal algebras. (English) Zbl 0878.03041
Fernández Stacco, Edgardo L. (ed.) et al., Proceedings of the 3rd conference of mathematics “Dr. Antonio A. R. Monteiro”, Bahía Blanca, Argentina, April 26-28, 1995. Bahía Blanca: Universidad Nacional del Sur, Dept. de Matemática, 69-78 (1996).
Summary: Four-valued modal algebras were introduced by A. Monteiro in 1978 as a generalization of the three-valued Lukasiewicz algebras, and they were studied by I. Loureiro [Algebras modais tetravalentes. Thesis. Fac. Ci. Lisboa (1983), C. R. Acad. Sci., Paris, Ser. I 295, 555-557 (1982; Zbl 0516.03010); see also A. Figallo, Rev. Unión Mat. Argent. 35, 61-65 (1990; Zbl 0816.06011), Port. Math. 49, 249-261 (1992; Zbl 0787.03060)]. In this paper, we define monadic four-valued modal algebras and we give a set of independent axioms for them. We study congruences and homomorphisms, showing that monadic four-valued modal algebras are semisimple, and, finally, we characterize the simple algebras.
Our results generalize those obtained by L. Monteiro [Algebras de Lukasiewicz trivalentes monadicas. Diss. Notas de logica matematica, No. 32, Bahia Blanca, Argentina (1974; Zbl 0298.02063)] for monadic three-valued Lukasiewicz algebras.
For the entire collection see [Zbl 0840.00019].
Our results generalize those obtained by L. Monteiro [Algebras de Lukasiewicz trivalentes monadicas. Diss. Notas de logica matematica, No. 32, Bahia Blanca, Argentina (1974; Zbl 0298.02063)] for monadic three-valued Lukasiewicz algebras.
For the entire collection see [Zbl 0840.00019].
MSC:
| 03G25 | Other algebras related to logic |
