On the Representation of Mathematical Concepts and their Translation into First-Order Logic

  • To prove difficult theorems in a mathematical field requires substantial know-ledge of that field. In this thesis a frame-based knowledge representation formal-ism including higher-order sorted logic is presented, which supports a conceptualrepresentation and to a large extent guarantees the consistency of the built-upknowledge bases. In order to operationalize this knowledge, for instance, in anautomated theorem proving system, a class of sound morphisms from higher-orderinto first-order logic is given, in addition a sound and complete translation ispresented. The translations are bijective and hence compatible with a later proofpresentation.In order to prove certain theorems the comprehension axioms are necessary,(but difficult to handle in an automated system); such theorems are called trulyhigher-order. Many apparently higher-order theorems (i.e. theorems that arestated in higher-order syntax) however are essentially first-order in the sense thatthey can be proved without the comprehension axioms: for proving these theoremsthe translation technique as presented in this thesis is well-suited.

Export metadata

  • Export Bibtex
  • Export RIS

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Manfred Kerber
URN (permanent link):urn:nbn:de:hbz:386-kluedo-3057
Serie (Series number):SEKI Report (92,8)
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Faculties / Organisational entities:Fachbereich Informatik
DDC-Cassification:004 Datenverarbeitung; Informatik

$Rev: 12793 $