- Claus-Peter Wirth
- Descente Infinie + Deduction
- Logic Journal of the IGPL,
Vol. 12(1), pp. 1-96, January 2004
- Oxford University Press
- Optimal. Accepted version, submitted September 12, 2003.
Only superficial corrigenda.
There is also an
- Inductive theorem proving in the form of descente infinie
was known to the ancient Greeks
and is the standard induction method of a working mathematician since it
was reinvented in the middle of the 17th century.
We present an integration of descente infinie
into state-of-the-art free-variable sequent and tableau calculi.
It is well-suited for
an efficient interplay of human interaction and automation
and combines raising,
explicit representation of dependence between variables,
the liberalized delta-rule,
preservation of solutions, and unrestricted applicability
of lemmas and induction hypotheses.
The semantical requirements are satisfied for a variety of two-valued logics,
such as clausal logic, classical first-order logic,
and higher-order modal logic.
- Full paper
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- Application for a DFG research grant; submitted June 30, 2004.
Rejected January 4, 2005; the reviews show no sign of any
knowledge on deduction, but of ignorance on induction only.
I would like to publish the whole evalution data as an example
for the DFG's inability to evaluate non-trivial proposals.
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some originally identical fonts are different in this version,
but the whole file can be searched!
- Related Talk
- Ceterum censeo Descente Infinie esse disputandam