Consistency proof via pointwise induction

NF consistency proof via construction of parent functions

parent function, definition be-gins, 26abstract parent function, definition com-pleted, 30allowable permutation, 28ambiguity, axiom scheme of, 13anomaly of a near litter, 34atom, irregular, 27atoms, regular, 26axiom of weak extensionality, 15axiom scheme of ambiguity, 13axioms of NF, 11axioms of TST, 8, 10 Choice false in NF, 13Choice, axiom o...

Inductionless Induction (aka Implicit Induction or Proof by Consistency): A Literature Survey

Von Neumann's Consistency Proof

In 1925, the twenty-one-year-old John von Neumann wrote and submitted a long paper, `Zur Hilbertschen Beweistheorie' (the paper would have been published two years later as von Neumann 1927), containing a consistency proof for a fragment of rst-order arithmetic (the fragment without induction and with the successor axioms only) by a variant of Hilbert's substitution method. A correct estimate o...

ARTIFICIAL INTELLIGENCE Proof by Consistency*

Advances of the past decade in methods and computer programs for showing consistency of proof systems based on first-order equations have made it feasible, in some settings, to use proof by consistency as an alternative to conventional rules of inference. Musser described the method applied to proof of properties of inductively defined objects. Refinements of this inductionless induction method...

Higher-Order Proof by Consistency

We investigate an integration of the rst order method of proof by consistency PBC also known as term rewriting induction into theorem proving in higher order speci cations PBC may be seen as well founded in duction over an ordering which contains the rewrite relation and in this paper we extend this method to the higher order rewrite relation due to Nipkow This yields a proof procedure which ha...