Formal definition of a general ontology pattern language using a graph grammar

In recent years, there has been a growing interest in the use of ontological theories in the philosophical sense (Foundational Ontologies) to analyze and (re)design conceptual modeling languages. This paper is about an ontologically well-founded conceptual modeling language in this tradition, termed OntoUML. This language embeds a number of ontological patterns that reflect the micro-theories comprising a particular foundational ontology named UFO. We here (re)define OntoUML as a formal graph grammar and demonstrate how the models of this language can be constructed by the combined application of ontological patterns following a number of graph transformation rules. As a result, we obtain a version of this language fully defined as a formal Ontology Pattern Grammar. In other words, this paper presents a formal definition of OntoUML that is both explicit in terms of the ontological patterns that it incorporates and is completely independent of the UML meta-model.