This paper concerns with the creation of a knowledge management ontology (in the open source OWL/Protégé environment), including all the concepts and both the explicit and impicit relations between the concepts met in the Platonic dialogue Parmenides. The selected part of Parmenides is the second half (137c4-166c6), where Parmenides undertakes to take on the challenge of exposing a Zenonian type argumentation concerning the properties of one and being. The incorporation of the Platonic concepts and relations to a software ontology gives the opportunity to organize the philosophical ideas of a certain context in an hierarchical tree enriched with the various defined relations, detect possible logical inconsistencies and produce automatically further concept relations.