Compatible Operations on Residuated Lattices

Studia Logica 98 (1-2):203-222 (2011)
  Copy   BIBTEX

Abstract

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

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,168

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2011-07-20

Downloads
35 (#335,639)

6 months
1 (#448,551)

Historical graph of downloads
How can I increase my downloads?