INVESTIGADORES
CASTIGLIONI JosÉ Luis
artículos
Título:
Compatible operations on commutative residuated lattices
Autor/es:
J.L. CASTIGLIONI; M. MENNI; M. SAGASTUME
Revista:
JOURNAL OF APPLIED NON-CLASSICAL LOGICS
Editorial:
Éditions Hermès-Lavoisier
Referencias:
Año: 2008 vol. 18 p. 413 - 425
ISSN:
1166-3081
Resumen:
Let $L$ be a commutative residuated lattice, and ${f:L^k o L}$ afunction. We give a necessary and sufficient condition for $f$ tobe compatible with respect to every congruence on $L$. We use thischaracterization of compatible functions in order to prove thatthe variety of commutative residuated lattices is locally affinecomplete. Then, we find conditions on a not necessarily polynomial function$P(x,y)$ in $L$ that imply that the function ${x mapsto  min{yin L mid P(x,y) leq y}}$ is compatible when defined. Inparticular, ${P_n(x,y) = y^n o x}$, for natural $n$, defines afamily, $S_n$, of compatible functions on some commutativeresiduated lattices. We show through examples that $S_1$ and$S_2$, defined respectively from $P_1$ and $P_2$, are independentas operations over this variety; i.e. neither $S_1$ is definableas a polynomial in the language of $L$ enriched with $S_2$ nor$S_2$ in that enriched with $S_1$.