Perfect residuated lattice ordered monoids

✍ Scribed by Jiří Rachůnek; Dana Šalounová

• Book ID: 111493125
• Publisher: SP Versita
• Year: 2010
• Tongue: English
• Weight: 198 KB
• Volume: 60
• Category: Article
• ISSN: 0139-9918
• DOI: 10.2478/s12175-010-0050-6

✦ Synopsis

Bounded R -monoids form a large subclass of the class of residuated lattices which contains certain of algebras of fuzzy and intuitionistic logics, such as GMV -algebras (= pseudo-MV -algebras), pseudo-BL-algebras and Heyting algebras. Moreover, GMV -algebras and pseudo-BL-algebras can be recognized as special kinds of pseudo-MV -effect algebras and pseudo-weak MV -effect algebras, i.e., as algebras of some quantum logics. In the paper, bipartite, local and perfect R -monoids are investigated and it is shown that every good perfect R -monoid has a state (= an analogue of probability measure).