Categorical grammars for processes modeling

Abstract

The diversity and heterogeneity of real-world systems makes it impossible to naturally model them only with existing modeling languages. For this reason, models are often constructed using domain specific modeling languages as metamodels, which must themselves be specified by meta-metamodels. In this paper we present a new approach, based on the category theory, to specify metamodels. A grammar for modeling processes (PN, CSP, EPC, etc.) syntactically defines processes and then presents a set of reaction rules that model the behavior of the system. We will see that the categorical sketch is sufficiently expressive to be able to support the constructions needed to visually define the syntax of a graphical modeling language. The category theory also provides appropriate structures to model the behavioral rules of a real system.