Diagrammatic logic applied to a parameterisation process

Authors:
CÉsar DomÍnguez;Dominique Duval
Affiliations:
Departamento de matemáticas y computación, universidad de la rioja, edificio vives, luis de ulloa s/n, e-26004 logroño, la rioja, spain email: cesar.dominguez@unirioja.es;Laboratoire jean kuntzmann, université de grenoble, 51 rue des mathématiques, bp 53, f-38041 grenoble cédex 9, france email: dominique.duval@imag.fr
Venue:
Mathematical Structures in Computer Science
Year:
2010

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Abstract

This paper provides an abstract definition of a class of logics, called diagrammatic logics, together with a definition of morphisms and 2-morphisms between them. The definition of the 2-category of diagrammatic logics relies on category theory, mainly on adjunction, categories of fractions and limit sketches. This framework is applied to the formalisation of a parameterisation process. This process, which consists of 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 parameterised specification and an actual parameter is shown to be a 2-morphism of logics.