Yoneda Philosophy in Engineering

Mathematical models, such as sets of equations, are used in engineering to represent and analyze the behaviour of physical systems. The conventional notations in formulating engineering models do not clearly provide all the details required in order to fully understand the equations, and, thus, artifacts such as ontologies, which are the building blocks of knowledge representation models, are used to fulfil this gap. Since ontologies are the outcome of an intersubjective agreement among a group of individuals about the same fragment of the objective world, their development and use are questions in debate with regard to their competencies and limitations to univocally conceptualize a domain of interest. This is related to the following question: “What is the criterion for delimiting the specification of the main identifiable entities in order to consistently build the conceptual framework of the domain in question?” This query motivates us to view the Yoneda philosophy as a fundamental concern of understanding the conceptualization phase of each ontology engineering methodology. In this way, we exploit the link between the notion of formal concepts of formal concept analysis and a concluding remark resulting from the Yoneda embedding lemma of category theory in order to establish a formal process. 1. Introduction In the computer science context, the terms ontology and concept are defined in many various ways, and sometimes their use is a confused mixture of both terms. On the one hand, an ontology is defined as a common conceptualization of a general idea, or a domain of interest [1, 2], while, on the other hand, a concept is defined as a general idea, which is created by removing the uncommon characteristics from several particular ideas [3]. Thus, it is obvious that ontologies use concepts to convey their semantics and concepts are definitional structures that are explicitly encoded within ontologies. In practice, an ontology consists of classes that are concepts of a particular domain, relations between classes, a hierarchy of classes, properties of classes that describe their attributes, instances of classes with specific values, and axioms that specify additional constraints over classes. So, the most crucial task of building an ontology is to consistently express its classes, that is, the concepts of a particular domain. An indispensable condition for formally expressing a concept that should carry a meaning, besides its name that does not carry any meaning, is to determine all its stakeholders, that is, other terms interrelated with the concept