A Note on a Parameterized Version of the Well-Founded Induction Principle
- The well-known and powerful proof principle by well-founded induction says that for verifying \(\forall x : P (x)\) for some property \(P\) it suffices to show \(\forall x : [[\forall y < x :P (y)] \Rightarrow P (x)] \) , provided \(<\) is a well-founded partial ordering on the domainof interest. Here we investigate a more general formulation of this proof principlewhich allows for a kind of parameterized partial orderings \(<_x\) which naturallyarises in some cases. More precisely, we develop conditions under which theparameterized proof principle \(\forall x : [[\forall y <_x x : P (y)] \Rightarrow P (x)]\) is sound in thesense that \(\forall x : [[\forall y <_x x : P (y)] \Rightarrow P (x)] \Rightarrow \forall x : P (x)\) holds, and givecounterexamples demonstrating that these conditions are indeed essential.
Author: | Bernhard Gramlich |
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URN: | urn:nbn:de:hbz:386-kluedo-3499 |
Series (Serial Number): | SEKI Report (95,8) |
Document Type: | Preprint |
Language of publication: | English |
Year of Completion: | 1995 |
Year of first Publication: | 1995 |
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 |