[FOM] relevant logic and paraconsistent logic
Arnon Avron
aa at tau.ac.il
Fri Mar 3 04:03:11 EST 2006
On Thu, Mar 02, 2006 at 04:42:17PM -0500, Neil Tennant wrote:
> If X is a consistent set of axioms, then any classical consequence of X
> can be proved from X in classical relevant logic (CR); and
> if X is a consistent set of axioms, then any intuitionistic consequence of
> X can be proved from X in intuitionistic relevant logic (IR).
Neil, I dont quite understand what you mean, and what is the exact
theorem you have in mind. As far as I remember, even relevant
arithmetics is very different from classical arithmetics, and quite weak
(I think Harvey can tell us about it. As far as I recall
he once solved one of the main open problems about relevant
arithmetics). In any case, what happens if X consists just of the
axioms {P, -P\/Q}? Classically (and intuitionistically) we can infer Q,
but in the usual relevant logics we cannot. I am sure that you know
this, so can you clarify your posting?
Arnon
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