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Mon, 03 Apr 2000 00:00:00 +0200Mon, 03 Apr 2000 00:00:00 +0200On the Representation of Mathematical Knowledge in Frames and its Consistency
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/278
We show how to buildup mathematical knowledge bases usingframes. We distinguish three differenttypes of knowledge: axioms, definitions(for introducing concepts like "set" or"group") 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.Manfred Kerberarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/278Mon, 03 Apr 2000 00:00:00 +0200Useful Properties of a Frame-Based Representation of Mathematical Knowledge
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/397
To prove difficult theorems in a mathematical field requires substantial know-ledge of that field. In this paper a frame-based knowledge representation formalismis presented, which supports a conceptual representation and to a large extent guar-antees the consistency of the built-up knowledge bases. We define a semantics ofthe representation by giving a translation into the underlaying logic.Manfred Kerberpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/397Mon, 03 Apr 2000 00:00:00 +0200