University of Vlora - Conference Center, ACA'10, Applications of Computer Algebra

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Representation issues regarding mathematical ontologies: why Description Logic does not suffice

Fred Freitas

Last modified: 2010-05-28

Abstract


In this work, we introduce with a discussion of the appropriate formalism to carry out the task of representing mathematical knowledge, and, particularly, the problems for relying on Description Logics for this task, departing from a concrete case study, an Ontology of Multilayer Perceptron Artificial Neural Network. The initial intent was to develop the ontology in the Semantic Web standardized language description logic OWL, which would offer us a lot of benefits, such as mature developing tools and reasoners, and a large community of users, etc. However, description logic is not expressive enough to represent complex mathematical constraints, for instance. Its grounding on set theoretic semantics allows the language mainly to describe precisely knowledge that involve sets, complex relations, not being endowed with the basic mathematical resources, like arithmetical operations, recursive functions and so on.