Intuitionistic second order propositional logic: Any sources?

From: Jan Burse <janburse@xxxxxxxxxxx>
Date: Sun, 01 Jun 2008 18:09:23 +0200

Dear All

It seems that intuitionistic logic, when equipped
with quantifiers that range over propositional
variables, becomes classical.

Because we can define:

f= forall p p
Etc..

Anybody knows approaches to second order propositional
logic which does not collapse this way?

Best Regards
.

Follow-Ups:
- Re: Intuitionistic second order propositional logic: Any sources?
  - From: Daryl McCullough
- Re: Intuitionistic second order propositional logic: Any sources?
  - From: Franz Binder
- Re: Intuitionistic second order propositional logic: Any sources?
  - From: Alan Smaill

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Re: Intuitionistic second order propositional logic: Any sources?
... Franz Binder schrieb: ... with quantifiers that range over propositional ... f= forall p p ... logic which does not collapse this way? ...
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Re: Intuitionistic second order propositional logic: Any sources?
... f= forall p p ... "Practical Foundations of Mathematics" contains a lot of theory about second order intuitionistic logic with a special emphasis to computing). ... The Coq proof assistant uses second order intuitionistic logic and really works (does not collapse): http://coq.inria.fr ... It uses a typed quantifiers. ...
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Re: Intuitionistic second order propositional logic: Any sources?
... Jan Burse says... ... with quantifiers that range over propositional ... f= forall p p ... Daryl McCullough ...
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Re: Intuitionistic second order propositional logic: Any sources?
... Daryl McCullough schrieb: ... with quantifiers that range over propositional ... f= forall p p ... have is ~~A -> A from this interpretation. ...
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... Ignore the bit about two quantifiers - I was following Arjen without ... character rather than just digits, ... your pattern doesn't have to match the whole line, ...
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