## Formal Definition of a General Ontology Pattern Language using a Graph Grammar

### Eduardo Zambon, Giancarlo Guizzardi

DOI: http://dx.doi.org/10.15439/2017F001

Citation: Proceedings of the 2017 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 11, pages 1–10 (2017)

Abstract. 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 \emph{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 \emph{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.

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