On 12/17/2012 11:53 PM, Quentin Anciaux wrote:
Is there a logic that does not recognize a proposition to be true or
unless there is an accessible proof for it? Accessible is hard for me to
canonically, but one could think of it as being able to build a model (via
constructive or none constructive means) of the proposition with a theory
extension thereof) that includes the proposition.
If you include the proposition as an axiom, then it is trivially true, but you don't
work anymore in the same theory as the one without that proposition as axiom.
It seems like just defining a new predicate "accessible" which means "provable or
disprovable" which you attach to propositions. Then it doesn't need be an axiom and it
still allows an excluded middle.
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