Abstract
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.
Highlights
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
In order to make the ontological status of concepts apparent, independently of the language used to express them and of the techniques used for embedding them within ontologies, we have exploited the link between the notion of formal concepts of formal concept analysis (FCA) and a concluding remark resulting from the Yoneda embedding lemma of category theory
A triadic approach to Formal concept analysis (FCA) has been designed, the so-called triadic concept analysis (TCA) [16], as another FCA extension, which is based on a formalization of the triadic relation connecting objects, attributes, and conditions, where a concept is described by its extension, intention, and modus, respectively [17]
Summary
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. In order to make the ontological status of concepts apparent, independently of the language used to express them and of the techniques used for embedding them within ontologies, we have exploited the link between the notion of formal concepts of formal concept analysis (FCA) and a concluding remark resulting from the Yoneda embedding lemma of category theory. This enables the formalization of concepts by considering their semantics, since the notion of a concept in computer science is very subtle and does not rely on mathematical constructors.
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