Computational Ontology for Geometry
John Kontos and Iosif Armaos
Department of Philosophy and History of Science,
National and Kapodistrian University of Athens,
HELLAS
ikontos2003@yahoo.com , iarmaos@otenet.gr
A system of computational ontology is presented that is useful for geometrical
discovery systems and geometrical tutoring systems. The geometrical entities and
processes are organised in an ontology implemented in prolog. Different kinds of
queries can be answered by the system concerning the relations between the entities
of the ontology. The ontology contains concepts relevant to both continuous and
discrete geometrical diagrams and proofs concerning these diagrams. A graphical
subsystem is implemented that demonstrates the ontological knowledge encoded in
the system. The ontology system is applied to the analysis of texts stating the proofs
of geometrical theory. The utility of the answering of ontological queries related to
these proof texts is illustrated.
Directions of the future development that concern geometric discovery and
geometrical tutoring are finally presented and related to the state of the art in the
field. The results obtained in the field of computational geometric reasoning illustrate
the use of unambiguous ontology and strict rules that apply to proofs which may
serve as models for correct scientific reasoning.