Diagrammatic logic applied to a parameterization process

TL;DR

This paper introduces diagrammatic logics using category theory and applies this framework to formalize a parameterization process, including parameter passing, as morphisms and 2-morphisms of logics.

Contribution

It provides an abstract categorical framework for diagrammatic logics and formalizes parameterization and parameter passing as morphisms within this framework.

Findings

Framework based on category theory for diagrammatic logics

Parameterization process formalized as a morphism of logics

Parameter passing modeled as a 2-morphism of logics

Abstract

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.