Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4663089 | Journal of Applied Logic | 2008 | 18 Pages |
Abstract
Extended-order algebras are defined, whose operation extends the order relation of a poset with a greatest element. Most implicative algebras, including Hilbert algebras and BCK algebras fall within this context. Several classes of extended-order algebras are considered that lead to most well known multiplicative ordered structures by means of adjunction, once the completion process due to MacNeille is applied. In particular, complete distributive extended-order algebras are considered as a generalization of complete residuated lattices, to provide a structure that suits quite well for many-valued mathematics.
Related Topics
Physical Sciences and Engineering
Mathematics
Logic
Authors
Cosimo Guido, Paola Toto,