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Abstract

"Der Begriff der Gleichheit ist uns Mathematikern vielleicht der geläufigste; dennoch läßt sich schwer sagen, was wir unter ihm verstehen." - Mit diesem Satz beginnt GERHARD HESSENBERG sein Buch über die .Grundlagen der Geometrie' ([24], Berlin, 1930, §1). Er kommt nach einer ausführlichen Diskussion zum Schluß, daß die Relation der Gleichheit nichts anderes als eine Äquivalenzrelation sei, also eine symmetrische, transitive und reflexive Relation, und daß auch umgekehrt jede symmetrische, transitive und reflexive Relation eine Gleichheitsbeziehung sei. Die Begriffe Gleichheit und Äquivalenz wären demnach synonym. Schaut man im .Mathematischen Wörterbuch' von J. NAAS & H.L. SCHMID (Berlin, 1967) nach, so findet man unter dem Stichwort Gleichheit (p. 639) genau dieselbe Definition: "Die Gleichheit ist eine Äquivalenzrelation und umgekehrt kann jede Äquivalenzrelation als eine besondere Art von Gleichheit aufgefaßt werden."

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Abstract

Several instruments of knowledge organization will reflect different possibilities for information retrieval. In this context, ontologies have a different potential because they allow knowledge discovery, which can be used to retrieve information in a more flexible way. However, this potential can be affected by the theoretical principles adopted in ontology building. The aim of this paper is to discuss, in an introductory way, how a (not exhaustive) set of theoretical principles can influence an aspect of ontologies: their use to obtain inferences. In this context, the role of Ingetraut Dahlberg's Theory of Concept is discussed. The methodology is exploratory, qualitative, and from the technical point of view it uses bibliographic research supported by the content analysis method. It also presents a small example of application as a proof of concept. As results, a discussion about the influence of conceptual definition on subsumption inferences is presented, theoretical contributions are suggested that should be used to guide the formation of hierarchical structures on which such inferences are supported, and examples are provided of how the absence of such contributions can lead to erroneous inferences