Compatible Operations on Residuated Lattices

Autor: H. J. San Martín, José Luis Castiglioni
Rok vydání: 2011
Předmět:
Zdroj: Studia Logica. 98:203-222
ISSN: 1572-8730
0039-3215
DOI: 10.1007/s11225-011-9333-3
Popis: 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 residuated lattice L which imply that the function $${x \mapsto min\{y \in L : P(x, y) \leq Q(x, y)\}}$$ when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators.
Databáze: OpenAIRE
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