Title :
Characterization theorem of lattice implication algebras
Author_Institution :
Sch. of Inf. Environ., Tokyo Denki Univ., Inzai, Japan
Abstract :
In this paper, we show the characterization theorem of lattice implication algebras. The algebras were presented by Xu (J. Southwest Jiaotong Univ., p.20-27) in 1993. Our theorem means that the class of all lattice implication algebras coincides with the class of all bounded commutative BCK-algebras. Hence lattice implication algebras are categorically equivalent to MV-algebras and to Wajsberg algebras.
Keywords :
algebra; Boolean algebra; MV-algebras; Wajsberg algebras; algebra class; bounded commutative BCK algebras; lattice implication algebras; Boolean algebra; Lattices; Logic functions;
Conference_Titel :
Multiple-Valued Logic, 2004. Proceedings. 34th International Symposium on
Print_ISBN :
0-7695-2130-4
DOI :
10.1109/ISMVL.2004.1319951
