Embedding Ontologies Using Category Theory Semantics



Ontologies are a formalization of a particular domain through a collection of axioms founded, usually, in Description Logic. Within its structure, the knowledge in the axioms contain semantic information of the domain and that fact has motivated the development of methods that capture such knowledge and, therefore, can perform different tasks such as prediction and similarity computation. Under the same motivation, we present a new method to capture semantic information from an ontology. We explore the logical component of the ontologies and their theoretical connections with their counterparts in Category Theory, as Category Theory develops a structural representation of mathematical systems and the structures found there have strong relationships with Logic founded in the so-called Curry-Howard-Lambek isomorphism. In this regard, we have developed a method that represents logical axioms as Categorical diagrams and uses the commutativity property of such diagrams as a constraint to generate embeddings of ontology classes in Rn. Furthermore, as a contribution in terms of software tools, we developed mOWL: Machine Learning Library With Ontologies. mOWL is a software library that incorporates methods in the state of the art, usually in Machine Learning, which utilizes ontologies as background knowledge. We rely on mOWL to implement the proposed method and compare it with the existing ones.
Date made available2022
PublisherKAUST Research Repository

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