Compatible operations on commutative residuated lattices
| Autor Principal: | |
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| Otros autores o Colaboradores: | , |
| Formato: | Capítulo de libro |
| Lengua: | inglés |
| Acceso en línea: | http://dx.doi.org/10.3166/jancl.18.413-425 Consultar en el Cátalogo |
| Resumen: | Let L be a commutative residuated lattice and let f : Lk → L a function. We give a necessary and sufficient condition for f to be compatible with respect to every congruence on L. We use this characterization of compatible functions in order to prove that the variety of commu- tative residuated lattices is locally affine complete. Then, we find conditions on a not necessarily polynomial function P (x, y) in L that imply that the function x → min{y ∈ L - P (x, y) ≤ y} is compatible when defined. In particular, Pn (x, y) = y n → x, for natural number n, defines a family, Sn , of compatible functions on some commutative residuated lattices. We show through examples that S1 and S2 , defined respectively from P1 and P2 , are independent as operations over this variety; i.e. neither S1 is definable as a polynomial in the language of L enriched with S2 nor S2 in that enriched with S1 . |
| Notas: | Formato de archivo: PDF. -- Este documento es producción intelectual de la Facultad de Informática - UNLP (Colección BIPA/Biblioteca) |
| Descripción Física: | 1 archivo (227,2 KB) |
| DOI: | 10.3166/jancl.18.413-425 |