APM  Vol.4 No.5 , May 2014
Epimorphisms between Finite 4-Valued Modal Algebras
ABSTRACT

In this paper, we determine conditions for the existence of an epimorphism between two finite 4-valued modal algebras and state a method to obtain it. Furthermore, we obtain formulas which generalize those indicated by R. Sikorski for finite Boolean algebras [1], and by M. Abad and A. V. Figallo for finite 3-valued ukasiewicz algebras [2].


Cite this paper
Figallo, A. , Pick, E. and Saad, S. (2014) Epimorphisms between Finite 4-Valued Modal Algebras. Advances in Pure Mathematics, 4, 222-227. doi: 10.4236/apm.2014.45029.
References
[1]   Sikorski, R. (1949) On the Inducing of Homomorphisms by Mappings. Fundamenta Mathematicae, 36, 7-22.

[2]   Abad, M. and Figallo, A.V. (1992) On the Lukasiewicz homomorphisms. Instituto de Ciencias Basicas, UNSJ, 1-12.

[3]   Loureiro, I. (1982) Axiomatisation et proprietes des algebres modales tetravalentes. C.R. Acad. Sc. Paris, t. 295, Serie I, 555-557.

[4]   Loureiro, I. (1984) Finite Tetravalent Modal Algebras. Revista de la Union Matematica Argentina, 31, 187-191.

[5]   Loureiro, I. (1983) Prime Spectrum of a Tetravalent Modal Algebras. Notre Dame Journal of Formal Logic, 24, 389-394.
http://dx.doi.org/10.1305/ndjfl/1093870382

[6]   Figallo, A.V. (1990) Notes on Generalized N-Lattices. Revista de la Union Matematica Argentina, 35, 61-65.

[7]   Figallo, A.V. (1992) On the Congruence in Four-Valued Modal Algebras. Portugaliae Mathematica, 49, 249-261.

[8]   Figallo, A.V. and Ziliani, A. (1991) Symmetric Tetra-Valued Modal Algebras. Notas de la Sociedad Matematica de Chile, 10, 133-141.

[9]   Ziliani, A. (1995) On Axioms and Properties of Monadic Four-Valued Algebras. Actas del Tercer Congreso Dr. A.R.R. Monteiro, Instituto de Matematica, U. N. del Sur, Argentina, 69-78.

[10]   Figallo A.V. and Landini, P. (1995) On Generalized I-Algebras and Modal 4-Valued Algebras. Reports on Mathematical Logic, 29, 3-18.

[11]   Font, J.M. and Rius, M. (2000) An Abstract Algebraic Logic Approach to Tetravalent Modal Logics. Journal of Symbolic Logic, 65, 481-518.
http://dx.doi.org/10.2307/2586552

[12]   Coniglio, M.E. and Figallo, M. (2013) Hilbert-Style Presentations of Two Logics Associated to Tetravalent Modal Algebras. Studia Logica, 102, 525-539.
http://dx.doi.org/10.1007/s11225-013-9489-0

[13]   Monteiro, A. (1960) Matrices de Morgan Caracteristiques Pour le Calcul Propositionnel Classique. Anais da Academia Brasileira de Ciências, 52, 1-7.

 
 
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