On the Representation of Mathematical Knowledge in Frames and its Consistency
Manfred Kerber · Publication Server of Kaiserslautern University of Technology (Kaiserslautern University of Technology) · 1999
We show how to buildup mathematical knowledge bases usingframes. We distinguish three differenttypes of knowledge: axioms, definitions(for introducing concepts like set orgroup) and theorems (for relating theconcepts). The consistency of such know-ledge bases cannot be proved in gen-eral, but we can restrict the possibilit-ies where inconsistencies may be impor-ted to very few cases, namely to the oc-currence of axioms. Definitions and the-orems should not lead to any inconsisten-cies because definitions form conservativeextensions and theorems are proved to beconsequences.