Diagrammatic logic applied to a parameterization process

Cesar Dominguez (1) , Dominique Duval (2)

1 Department of Mathematics and Computer Science - Departamento de Matematicas y Computacion
2 CASYS - Calculs Algébriques et Systèmes Dynamiques

This paper provides an abstract definition of some kinds of logics, called diagrammatic logics, together with a definition of morphisms and of 2-morphisms between diagrammatic logics. The definition of the 2-category of diagrammatic logics rely on category theory, mainly on adjunction, categories of fractions and limit sketches. This framework is applied to the formalization of a parameterization process. This process, which consists in adding a formal parameter to some operations in a given specification, is presented as a morphism of logics. Then the parameter passing process, for recovering a model of the given specification from a model of the parameterized specification and an actual parameter, is seen as a 2-morphism of logics.

Mots clés: Diagrammatic logic; categories; sketches; computer algebra; parameterization process

Domaines: Logique en informatique [cs.LO]; Catégories et ensembles [math.CT]

Cesar Dominguez, Dominique Duval. Diagrammatic logic applied to a parameterization process. Mathematical Structures in Computer Science, 2010, 20 (4), pp.639-654. ⟨10.1017/S0960129510000150⟩. ⟨hal-00411069⟩