New types of hyper MV-deductive systems in hyper MV-algebras

2010 ◽  
Vol 56 (4) ◽  
pp. 400-405 ◽  
Author(s):  
Young Bae Jun ◽  
Min Su Kang ◽  
Hee Sik Kim
Keyword(s):  
Deductive Systems ◽  
Mv Algebras

scholarly journals Fuzzy structures of hyper-MV-deductive systems in hyper-MV-algebras

2010 ◽  
Vol 59 (8) ◽  
pp. 2982-2989 ◽  
Author(s):  
Young Bae Jun ◽  
Min Su Kang ◽  
Hee Sik Kim
Keyword(s):  
Deductive Systems ◽  
Mv Algebras

scholarly journals Monadic pseudo BE-algebras

2020 ◽  
Vol 70 (5) ◽  
pp. 1013-1040
Author(s):  
Lavinia Corina Ciungu
Keyword(s):  
Deductive Systems ◽  
One To One ◽  
Universal Quantifiers ◽  
Mv Algebras

AbstractIn this paper we define the monadic pseudo BE-algebras and investigate their properties. We prove that the existential and universal quantifiers of a monadic pseudo BE-algebra form a residuated pair. Special properties are studied for the particular case of monadic bounded commutative pseudo BE-algebras. Monadic classes of pseudo BE-algebras are investigated and it is proved that the quantifiers on bounded commutative pseudo BE-algebras are also quantifiers on the corresponding pseudo MV-algebras. The monadic deductive systems and monadic congruences of monadic pseudo BE-algebras are defined and their properties are studied. It is proved that, in the case of a monadic distributive commutative pseudo BE-algebra there is a one-to-one correspondence between monadic congruences and monadic deductive systems, and the monadic quotient pseudo BE-algebra algebra is also defined.

scholarly journals Ideals in residuated lattices

2021 ◽  
Vol 37 (1) ◽  
pp. 53-63
Author(s):  
DUMITRU BUŞNEG ◽  
DANA PICIU ◽  
ANCA-MARIA DINA
Keyword(s):  
Fuzzy Sets ◽  
Binary Relation ◽  
Congruence Relation ◽  
Natural Generalization ◽  
Residuated Lattices ◽  
Algebraic Analysis ◽  
Deductive Systems ◽  
Mv Algebra ◽  
The Relationship ◽  
Mv Algebras

"The notion of ideal in residuated lattices is introduced in [Kengne, P. C., Koguep, B. B., Akume, D. and Lele, C., L-fuzzy ideals of residuated lattices, Discuss. Math. Gen. Algebra Appl., 39 (2019), No. 2, 181–201] and [Liu, Y., Qin, Y., Qin, X. and Xu, Y., Ideals and fuzzy ideals in residuated lattices, Int. J. Math. Learn & Cyber., 8 (2017), 239–253] as a natural generalization of that of ideal in MV algebras (see [Cignoli, R., D’Ottaviano, I. M. L. and Mundici, D., Algebraic Foundations of many-valued Reasoning, Trends in Logic-Studia Logica Library 7, Dordrecht: Kluwer Academic Publishers, 2000] and [Chang, C. C., Algebraic analysis of many-valued logic, Trans. Amer. Math. Soc., 88 (1958), 467–490]). If A is an MV algebra and I is an ideal on A then the binary relation x ∼I y iff x^{*}Ꙩ y; x Ꙩy^{*} ∈ I , for x; y ∈ A; is a congruence relation on A. In this paper we find classes of residuated lattices for which the relation ∼ I (defined for MV algebras) is a congruence relation and we give new characterizations for i-ideals and prime i-ideals in residuated lattices. As a generalization of the case of BL algebras (see [Lele, C. and Nganou, J. B., MV-algebras derived from ideals in BL-algebras, Fuzzy Sets and Systems, 218 (2013), 103–113]), we investigate the relationship between i-ideals and deductive systems in residuated lattices."

scholarly journals HYPER MV-DEDUCTIVE SYSTEMS OF HYPER MV-ALGEBRAS

2010 ◽  
Vol 25 (4) ◽  
pp. 537-545 ◽  
Author(s):  
Young-Bae Jun ◽  
Min-Su Kang ◽  
Hee-Sik Kim
Keyword(s):  
Deductive Systems ◽  
Mv Algebras

Metatheories of deductive systems

2004 ◽  
Author(s):  
Sergei V. Babyonyshev
Keyword(s):  
Deductive Systems

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.

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