Compatible operations on residuated lattices

J.L. CASTIGLIONI; SAN MARTIN, H.J.

STUDIA LOGICA

Springer

Año: 2011 vol. 98 p. 203 - 222

0039-3215

This work extend to residuated lattices the results of [7]. It also provides a possible generalization to this context of frontal operators in the sense of [9]. Let L be a residuated lattice, and f : L^k -> 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 residuated lattices is locally affine complete. We study some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P(x; y) and Q(x; y) on a esiduated lattice L which imply that certain function, when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators. We study some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P(x; y) and Q(x; y) on a esiduated lattice L which imply that certain function, when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators. We study some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P(x; y) and Q(x; y) on a esiduated lattice L which imply that certain function, when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators. We study some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P(x; y) and Q(x; y) on a esiduated lattice L which imply that certain function, when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators. We study some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P(x; y) and Q(x; y) on a esiduated lattice L which imply that certain function, when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators. We study some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P(x; y) and Q(x; y) on a esiduated lattice L which imply that certain function, when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators. We study some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P(x; y) and Q(x; y) on a esiduated lattice L which imply that certain function, when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators. L be a residuated lattice, and f : L^k -> 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 residuated lattices is locally affine complete. We study some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P(x; y) and Q(x; y) on a esiduated lattice L which imply that certain function, when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators.P(x; y) and Q(x; y) on a esiduated lattice L which imply that certain function, when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators.