Semi-simple and complete MV-algebras

1992 ◽  
Vol 29 (1) ◽  
pp. 1-9 ◽  
Author(s):  
L. P. Belluce
Keyword(s):  
Mv Algebras

scholarly journals Residuated Structures and Orthomodular Lattices

Studia Logica ◽  
2021 ◽  
Author(s):  
D. Fazio ◽  
A. Ledda ◽  
F. Paoli
Keyword(s):  
Algebraic Logic ◽  
Residuated Lattices ◽  
Quantum Structures ◽  
Heyting Algebras ◽  
Quantum Algebras ◽  
Orthomodular Lattices ◽  
Lattice Of Subvarieties ◽  
Residuated Structures ◽  
Common Framework ◽  
Mv Algebras

AbstractThe variety of (pointed) residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., $$\ell $$ ℓ -groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated $$\ell $$ ℓ -groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated $$\ell $$ ℓ -groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some parts of the theory of join-completions of residuated $$\ell $$ ℓ -groupoids to the left-residuated case, giving a new proof of MacLaren’s theorem for orthomodular lattices.

scholarly journals Priestley duality for MV-algebras and beyond

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wesley Fussner ◽  
Mai Gehrke ◽  
Samuel J. van Gool ◽  
Vincenzo Marra
Keyword(s):  
Large Class ◽  
Order Conditions ◽  
Enriched Environment ◽  
Priestley Duality ◽  
Distributive Lattices ◽  
First Order ◽  
Dual Spaces ◽  
Binary Operations ◽  
New Perspective ◽  
Mv Algebras

Abstract We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of the duality may more often be rendered as first-order conditions on dual spaces. In particular, we specialize our general results to the variety of MV-algebras, obtaining a duality for these in which the equations axiomatizing MV-algebras are dualized as first-order conditions.

Riesz–McNaughton functions and Riesz MV-algebras of nonlinear functions

2017 ◽  
Vol 311 ◽  
pp. 1-14 ◽  
Author(s):  
Antonio Di Nola ◽  
Giacomo Lenzi ◽  
Gaetano Vitale
Keyword(s):  
Nonlinear Functions ◽  
Mv Algebras ◽  
Mcnaughton Functions

scholarly journals Boolean Products of MV-Algebras: Hypernormal MV-Algebras

1996 ◽  
Vol 199 (3) ◽  
pp. 637-653 ◽  
Author(s):  
Roberto Cignoli ◽  
Antoni Torrens Torrell
Keyword(s):  
Boolean Products ◽  
Mv Algebras

Measures on MV-algebras

2002 ◽  
Vol 7 (2) ◽  
pp. 130-137 ◽  
Author(s):  
R. Frič
Keyword(s):  
Mv Algebras

Ideals and congruences in quasi-pseudo-MV algebras

2017 ◽  
Vol 22 (12) ◽  
pp. 3879-3889 ◽  
Author(s):  
Wenjuan Chen ◽  
Wieslaw A. Dudek
Keyword(s):  
Mv Algebras

Weak pseudo-Wajsberg and weak pseudo-MV algebras

2001 ◽  
Vol 5 (5) ◽  
pp. 334-346 ◽  
Author(s):  
R. Ceterchi
Keyword(s):  
Mv Algebras

An alternative construction of graphs by associating with algorithmic approach on MV-algebras

2021 ◽  
Vol 25 (21) ◽  
pp. 13201-13212
Author(s):  
Arif Gursoy ◽  
Necla Kircali Gursoy ◽  
Tahsin Oner ◽  
Ibrahim Senturk
Keyword(s):  
Algorithmic Approach ◽  
Alternative Construction ◽  
Mv Algebras

Perfect MV-algebras and their Logic

2007 ◽  
Vol 15 (1-2) ◽  
pp. 135-151 ◽  
Author(s):  
Lawrence P. Belluce ◽  
Antonio Di Nola ◽  
Brunella Gerla
Keyword(s):  
Mv Algebras

Perfect residuated lattice ordered monoids

2010 ◽  
Vol 60 (6) ◽  
Author(s):  
Jiří Rachůnek ◽  
Dana Šalounová
Keyword(s):  
Probability Measure ◽  
Residuated Lattice ◽  
Residuated Lattices ◽  
Heyting Algebras ◽  
Effect Algebras ◽  
Quantum Logics ◽  
Mv Algebras ◽  
Intuitionistic Logics

AbstractBounded Rℓ-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 Rℓ-monoids are investigated and it is shown that every good perfect Rℓ-monoid has a state (= an analogue of probability measure).

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