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Titel: On the Representation of Mathematical Concepts and their Translation into First-Order Logic
VerfasserIn: Kerber, Manfred
Sprache: Englisch
Erscheinungsjahr: 1992
Erscheinungsort: Kaiserslautern
DDC-Sachgruppe: 004 Informatik
Dokumenttyp: Forschungsbericht (Report zu Forschungsprojekten)
Abstract: To prove difficult theorems in a mathematical field requires substantial knowledge of that field. In this thesis a frame-based knowledge representation formalism including higher-order sorted logic is presented, which supports a conceptual representation and to a large extent guarantees the consistency of the built-up knowledge bases. In order to operationalize this knowledge, for instance, in an automated theorem proving system, a class of sound morphisms from higher-order into first-order logic is given, in addition a sound and complete translation is presented. The translations are bijective and hence compatible with a later proof presentation. In order to prove certain theorems the comprehension axioms are necessary, (but difficult to handle in an automated system); such theorems are called truly higher-order. Many apparently higher-order theorems (i.e. theorems that are stated in higher-order syntax) however are essentially first-order in the sense that they can be proved without the comprehension axioms: for proving these theorems the translation technique as presented in this thesis is well-suited.
Link zu diesem Datensatz: urn:nbn:de:bsz:291--ds-407971
hdl:20.500.11880/37673
http://dx.doi.org/10.22028/D291-40797
Schriftenreihe: SEKI-Report / Deutsches Forschungszentrum für Künstliche Intelligenz, DFKI [ISSN 1437-4447]
Band: 92,8
Datum des Eintrags: 21-Mai-2024
Fakultät: SE - Sonstige Einrichtungen
Fachrichtung: SE - DFKI Deutsches Forschungszentrum für Künstliche Intelligenz
Professur: SE - Sonstige
Sammlung:SciDok - Der Wissenschaftsserver der Universität des Saarlandes



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