[FOM] Feasible consistency---Truth Transfer Policy
V.Sazonov at csc.liv.ac.uk
Sat Oct 28 13:50:43 EDT 2006
Quoting Mirco Mannucci <mmannucc at cs.gmu.edu> Tue, 24 Oct 2006:
> LOGICAL RULES ARE CREDIBILITY VALUES TRANSFER OPERATORS,
> from the premisses to the consequences.
> Now, I think this transfer should be made explicit by what I like to
> call a TRUTH TRANSFER POLICY
> (TTP). A TTP prescribes which credibility for a specific rule (say
> ^-introduction in
> Natural Deduction) one should assign to the consequents, knowing the
> credibility of
> the antecedents.
I have doubts in such an approach which, as you want, does not restrict
logic, but only introduces a credibility values *via TTP*.
You know, the following is formally (in fact, feasibly) consistent:
M(0), forall x (M(x) => M(x+1)) and not M(100).
(A kind of solution of Heap Paradox.) Here M (meaning intuitively
'medium number') is a formally definable predicate in an appropriately
formalised theory of feasible numbers in a suitably restricted logic.
In fact closure under successor also means that it is impossible to
show which exactly is the borderline x where M(x) & not M(x+1) holds.
(There is some other unusual effect. The details, which are quite
rigorous, are omitted.)
Which should be TTP for Modus Ponens which would guarantee such a
consistency in terms of credibility in the case of classical logic
As I wrote in a previous posting, credibility values can be introduced,
but in a different way (via complexity of cut elimination or, more
properly speaking, complexity of elimination of abbreviations for
terms) which does not seem to be definable in terms of TTP.
P.S. I do not think that the subject 'paraconsistency' was
appropriate for this discussion.
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