Compatible Operations on Residuated Lattices
Studia Logica 98 (1-2):203-222 (2011)
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 operatorsDOI
10.1007/s11225-011-9333-3
My notes
Similar books and articles
Closure operators and complete embeddings of residuated lattices.Hiroakira Ono - 2003 - Studia Logica 74 (3):427 - 440.
Equational bases for joins of residuated-lattice varieties.Nikolaos Galatos - 2004 - Studia Logica 76 (2):227 - 240.
Free-decomposability in Varieties of Pseudocomplemented Residuated Lattices.D. Castaño, J. P. Díaz Varela & A. Torrens - 2011 - Studia Logica 98 (1-2):223-235.
A proof of standard completeness for Esteva and Godo's logic MTL.Sándor Jenei & Franco Montagna - 2002 - Studia Logica 70 (2):183-192.
Varieties of Commutative Integral Bounded Residuated Lattices Admitting a Boolean Retraction Term.Roberto Cignoli & Antoni Torrens - 2012 - Studia Logica 100 (6):1107-1136.
On a Definition of a Variety of Monadic ℓ-Groups.José Luis Castiglioni, Renato A. Lewin & Marta Sagastume - 2014 - Studia Logica 102 (1):67-92.
Crawley Completions of Residuated Lattices and Algebraic Completeness of Substructural Predicate Logics.Hiroakira Ono - 2012 - Studia Logica 100 (1-2):339-359.
Analytics
Added to PP
2011-07-20
Downloads
35 (#335,639)
6 months
1 (#448,551)
2011-07-20
Downloads
35 (#335,639)
6 months
1 (#448,551)
Historical graph of downloads
Citations of this work
Relatively compatible operations in BCK-algebras and some related algebras.N. Lubomirsky, H. J. San Martín & W. J. Zuluaga Botero - 2017 - Logic Journal of the IGPL 25 (3):348-364.
On Principal Congruences in Distributive Lattices with a Commutative Monoidal Operation and an Implication.Ramon Jansana & Hernán Javier San Martín - 2019 - Studia Logica 107 (2):351-374.
References found in this work
The modalized Heyting calculus: a conservative modal extension of the Intuitionistic Logic ★.Leo Esakia - 2006 - Journal of Applied Non-Classical Logics 16 (3-4):349-366.
An algebraic approach to intuitionistic connectives.Xavier Caicedo & Roberto Cignoli - 2001 - Journal of Symbolic Logic 66 (4):1620-1636.
On some new intuitionistic propositional connectives. I.Dov M. Gabbay - 1977 - Studia Logica 36 (1-2):127 - 139.
Implicit connectives of algebraizable logics.Xavier Caicedo - 2004 - Studia Logica 78 (1-2):155 - 170.