BL-algebras were introduced by P. Hajek as algebraic structures of Basic Logic. The aim of the paper is a survey of known results about the structure of finite BL-algebras and natural dualities for varieties of BL-algebras. Extending the notion of ordinal sum of BL-algebras, a class of finite BL-algebras, actually BL-comets, which can be seen as a generalization of finite BL-chain, is characterized. Then, just using BL-comets, any finite BL-algebra can be represented as a direct product of BL-comets. This result can be seen as a generalization of the representation of finite MV-algebras as a direct product of finite MV-chains. Then it is shown the existence of a strong duality for each variety generated by one finite non-trivial totally ordered BL-algebra. As an application of the dualities, the injective and the weak injective members of these classes are described.
Finiteness based results in BL-algebras / DI NOLA, A; Lettieri, Ada. - In: SOFT COMPUTING. - ISSN 1432-7643. - STAMPA. - 9:12(2005), pp. 889-896. [10.1007/s00500-004-0447-7]
Finiteness based results in BL-algebras
LETTIERI, ADA
2005
Abstract
BL-algebras were introduced by P. Hajek as algebraic structures of Basic Logic. The aim of the paper is a survey of known results about the structure of finite BL-algebras and natural dualities for varieties of BL-algebras. Extending the notion of ordinal sum of BL-algebras, a class of finite BL-algebras, actually BL-comets, which can be seen as a generalization of finite BL-chain, is characterized. Then, just using BL-comets, any finite BL-algebra can be represented as a direct product of BL-comets. This result can be seen as a generalization of the representation of finite MV-algebras as a direct product of finite MV-chains. Then it is shown the existence of a strong duality for each variety generated by one finite non-trivial totally ordered BL-algebra. As an application of the dualities, the injective and the weak injective members of these classes are described.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.