I wrote already that I am 1/4 greek, but proof is proof,
either informal or formal, in either case something is
established that is irrefutable.
Refutable are credulous conjectures. But sceptical proofs
are irrefutable. What you probably mean is falsification
of axioms.
Credulous and Sceptical Argumentation
(Prolog Implementation)
by D. Gaertner and F. Toni
http://www.doc.ic.ac.uk/~ft/CaSAPI/
Formally for toying around with the two modes of reasoning,
you can use the signs |= and |~.
You can define sceptical (usual FOL reasoning etc..) as follows:
A |= B :<=> forall M(M[A]=1 -> M[B]=1)
You can define credulous as follows:
A |~ B :<=> exists M(M[A]=1 & M[B]=1)
Here is an example of credulous reasoning:
a v b |~ a & b
Which is not possible in skeptical reasoning.
John Gabriel schrieb: