Information Sciences: an International Journal
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Mathematical fuzzy logic as a tool for the treatment of vague information
Information Sciences: an International Journal
Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics
Information Sciences: an International Journal
Filters of residuated lattices and triangle algebras
Information Sciences: an International Journal
On filter theory of residuated lattices
Information Sciences: an International Journal
Information Sciences: an International Journal
Observables on quantum structures
Information Sciences: an International Journal
Hi-index | 0.07 |
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 monoidal operation is restricted to those pairs that fulfil a certain extremality condition, and else left undefined. The subsequent construction applied to the partial algebra is easy, transparent, and leads directly to the structure needed for representation. In this paper, we consider subreducts of residuated lattices, the monoidal and the meet operation being dropped: the resulting algebras are pseudo-BCK semilattices. Assuming divisibility, we can pass on to partial algebras also in this case. To reconstruct the underlying group structure from this partial algebra, if applicable, is again straightforward. We demonstrate the elegance of this method for two classes of pseudo-BCK semilattices: semilinear divisible pseudo-BCK algebras and cone algebras.