# Graphol: A Graphical Language for Ontology Modeling Equivalent to OWL 2
## 1 Introduction  
There is a long tradition in many areas of computer science of conceptualizing domains of interest in terms of classes and relationships using a graphical or diagrammatic model. Consider, for example, ER (entity-relationship) diagrams [1], ubiquitously used in databases, or UML class diagrams [2], the de facto standard in software engineering for information modeling (when used as conceptual models rather than to represent software components). While often such diagrams are used in a semi-formal way to help communication, it is well-recognized that having precise semantics is actually needed to avoid ambiguities in design.  
Interestingly, the very first conceptual languages developed in AI were also graphical, most prominently semantic networks [3; 4]. However, most work on knowledge representation in AI has focused more on automated reasoning, and has gradually abandoned the graphical conceptual languages in favor of logical languages. This process has started with the famous paper \"What's in a link\" [5], which questioned the inherent ambiguity of graphical conceptual languages of the time, and has continued with the work on KL-ONE [6], then followed by the introduction of modern description logics (DLs) [7]. Nevertheless, by the early 1990s, a research program started to emerge: not to disregard, but to try to logically reconstruct graphical conceptual models used in many fields, such as software development and information systems, in order to enable automated reasoning on them [8; 9; 10]. This program has actually been one of the thrusts towards more and more expressive DLs [11] that ultimately led to the development of OWL and OWL 2 [12].  
In this paper we bring about a novel contribution to this program: we study a graphical formalism, called Graphol, which resembles ER and UML class diagrams, but has inherent formal semantics based on DLs and is able to fully capture the ontology language OWL 2. Our proposal comes after a few years of experience in ontology modeling in IT organizations that are knowledgeable on information systems and software engineering, so are familiar with UML and ER, but have only a technological view of ontology languagessuch as OWL 2 (e.g., [13; 14; 15]). In these contexts, people often struggle to effectively use the logical formalisms through which ontologies are typically specified, thus slowing down the adoption of semantic technologies. Graphol mitigates this problem, since it provides IT people with a formalism for specifying and reading ontologies rooted in conceptual modeling languages they are used to. Indeed, its usage has helped substantially in taking up semantic technologies in the industrial use cases [16; 17; 18; 19; 20; 21].  
We point out that we have also developed tools for drawing Graphol diagrams and translating them into standard OWL 2 ontology format. These tools, however, are not treated in depth in this paper, and we refer the reader to [22; 23] and to the Github repository of the Eddy ontology editor ([[https://github.com/obdasystems/eddy](https://github.com/obdasystems/eddy)]([https://github.com/obdasystems/eddy](https://github.com/obdasystems/eddy)), accessed on 17 January 2022) for the details. Here, instead, we study Graphol as a language, and focus on its formal properties. Specifically, we give its mathematical semantics, based on DLs, and show that Graphol diagrams can be translated into OWL 2 ontologies and vice versa. Furthermore, we describe a user evaluation study we carried out to verify the usability of our language. A preliminary version of some of the contributions given in this paper can be found in [24].