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doi:10.22028/D291-40797
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 |
Dateien zu diesem Datensatz:
Datei | Beschreibung | Größe | Format | |
---|---|---|---|---|
SEKI-Report-SR-92-08_Kerber_On-the-Representation-of-Mathematical-Concepts-and-their-Translation-into-First=Order-Logic.pdf | 7,92 MB | Adobe PDF | Öffnen/Anzeigen |
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