# Compatible operations on commutative weak residuated lattices

Compatibility of functions is a classical topic in Universal Algebra related to the notion of affine completeness. In algebraic logic, it is concerned with the possibility of implicitly defining new connectives. In this paper, we give characterizations of compatible operations in a variety of algebr...

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Autor principal: Articulo Inglés 2015 http://sedici.unlp.edu.ar/handle/10915/139191 Aportado por : SEDICI (UNLP) de Universidad Nacional de La Plata .
id I19-R120-10915-139191 dspace I19-R120-10915-1391912022-07-08T20:04:36Z http://sedici.unlp.edu.ar/handle/10915/139191 issn:0002-5240 issn:1420-8911 Compatible operations on commutative weak residuated lattices San Martín, Hernán Javier 2015-02-05 2022-07-08T17:55:57Z en Matemática commutative residuated lattices weak Heyting algebras congruences compatible functions Compatibility of functions is a classical topic in Universal Algebra related to the notion of affine completeness. In algebraic logic, it is concerned with the possibility of implicitly defining new connectives. In this paper, we give characterizations of compatible operations in a variety of algebras that properly includes commutative residuated lattices and some generalizations of Heyting algebras. The wider variety considered is obtained by weakening the main characters of residuated lattices (A, ∧, ∨, ·, →, e) but retaining most of their algebraic consequences, and their algebras have a commutative monoidal structure. The order-extension principle a ≤ b if and only if a → b ≥ e is replaced by the condition: if a ≤ b, then a → b ≥ e. The residuation property c ≤ a → b if and only if a · c ≤ b is replaced by the conditions: if c ≤ a → b , then a · c ≤ b, and if a · c ≤ b, then e → c ≤ a → b. Some further algebraic conditions of commutative residuated lattices are required. Facultad de Ciencias Exactas Articulo Articulo http://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International (CC BY 4.0) application/pdf 143-155 Universidad Nacional de La Plata I-19 R-120 SEDICI (UNLP) Inglés Matemática commutative residuated lattices weak Heyting algebras congruences compatible functions Matemática commutative residuated lattices weak Heyting algebras congruences compatible functions San Martín, Hernán Javier Compatible operations on commutative weak residuated lattices Matemática commutative residuated lattices weak Heyting algebras congruences compatible functions Compatibility of functions is a classical topic in Universal Algebra related to the notion of affine completeness. In algebraic logic, it is concerned with the possibility of implicitly defining new connectives. In this paper, we give characterizations of compatible operations in a variety of algebras that properly includes commutative residuated lattices and some generalizations of Heyting algebras. The wider variety considered is obtained by weakening the main characters of residuated lattices (A, ∧, ∨, ·, →, e) but retaining most of their algebraic consequences, and their algebras have a commutative monoidal structure. The order-extension principle a ≤ b if and only if a → b ≥ e is replaced by the condition: if a ≤ b, then a → b ≥ e. The residuation property c ≤ a → b if and only if a · c ≤ b is replaced by the conditions: if c ≤ a → b , then a · c ≤ b, and if a · c ≤ b, then e → c ≤ a → b. Some further algebraic conditions of commutative residuated lattices are required. Articulo Articulo San Martín, Hernán Javier San Martín, Hernán Javier San Martín, Hernán Javier Compatible operations on commutative weak residuated lattices Compatible operations on commutative weak residuated lattices Compatible operations on commutative weak residuated lattices Compatible operations on commutative weak residuated lattices Compatible operations on commutative weak residuated lattices compatible operations on commutative weak residuated lattices 2015 http://sedici.unlp.edu.ar/handle/10915/139191 AT sanmartinhernanjavier compatibleoperationsoncommutativeweakresiduatedlattices 1741622786898526208