A Mathematical Knowledge Base for Proving Theorems in Semigroup and Automata Theory
- We present a mathematical knowledge base containing the factual know-ledge of the first of three parts of a textbook on semi-groups and automata,namely "P. Deussen: Halbgruppen und Automaten". Like almost all math-ematical textbooks this textbook is not self-contained, but there are somealgebraic and set-theoretical concepts not being explained. These concepts areadded to the knowledge base. Furthermore there is knowledge about the nat-ural numbers, which is formalized following the first paragraph of "E. Landau:Grundlagen der Analysis".The data base is written in a sorted higher-order logic, a variant of POST ,the working language of the proof development environment OmegaGamma mkrp. We dis-tinguish three different types of knowledge: axioms, definitions, and theorems.Up to now, there are only 2 axioms (natural numbers and cardinality), 149definitions (like that for a semi-group), and 165 theorems. The consistency ofsuch knowledge bases cannot be proved in general, but inconsistencies may beimported only by the axioms. Definitions and theorems should not lead to anyinconsistency since definitions form conservative extensions and theorems areproved to be consequences.
Author: | Barbara Schütt, Manfred Kerber |
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URN: | urn:nbn:de:hbz:386-kluedo-3952 |
Series (Serial Number): | SEKI Report Working Papers (1993,2) |
Document Type: | Preprint |
Language of publication: | English |
Year of Completion: | 1999 |
Year of first Publication: | 1999 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2000/04/03 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Informatik |
DDC-Cassification: | 0 Allgemeines, Informatik, Informationswissenschaft / 004 Informatik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |