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Pseudo-BCK algebras as partial algebras

open access: yes, 2009
It is well-known that the representation of several classes of residuated lattices involves lattice-ordered groups. An often applicable method to determine the representing group (or groups) from a residuated lattice is based on partial algebras: the ...
Thomas Vetterlein
core  

Basic Logic, SMT solvers and finitely generated varieties of GBL-algebras

open access: yes, 2014
Basic Logic was introduced by Petr Hájek to provide a unified approach to fuzzy logics, and judging by its rapid adoption in the research community, it has enjoyed considerable success in this regard. One of the reasons is that while it is a very general
Peter Jipsen
core  
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States on semi-divisible generalized residuated lattices reduce to states on MV-algebras

Fuzzy Sets and Systems, 2008
The authors continue their study of the set MV\((L)\) of complemented elements of a residuated lattice \(L\) [Soft Comput. 12, No.~4, 353--357 (2008; Zbl 1138.06006)]. Such structures are related to mathematical fuzzy logic as well as to extended probability theory.
Esko Turunen
exaly   +3 more sources

Classes of examples of pseudo-MV algebras, pseudo-BL algebras and divisible bounded non-commutative residuated lattices

Soft Computing, 2009
There are close connections between pseudo MV-algebras (pseudo Wajsberg algebras) on the one hand and pseudo BL-algebras (pseudo Hájek (pP) algebras) and divisible noncommutative residuated lattices (divisible bounded reverse left-pseudo-BCK(pP) lattices) on the other hand, which generalize to the noncommutative case the close connections between MV ...
exaly   +2 more sources

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