# Questions tagged [intuitionistic-logic]

Intuitionistic logic refer constructive logic, a logical system avoiding deduction rules like *Reductio ad absurdum*.

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### How can infinitesimals be invertible in SIA?

I read that infinitesimals in SIA can be invertible: https://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis In typical models of smooth infinitesimal analysis, the infinitesimals are not ...
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### Do the monotone maps from a poset into a Heyting algebra form a Heyting algebra?

I am interested in generalizing the fact that the up-sets of a poset always form a Heyting algebra. Let $P$ be a poset and $H$ a Heyting algebra. $\operatorname{Hom}(P,H)$ can be made a bound lattice ...
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### Question on Intuitionistic Modal Logic

In the intuitionistic version of the modal logic K (IK), the following is a theorem: $(\Diamond p \to \Box q) \to \Box( p \to q)$. However, given the definitions for $\Box$ and $\Diamond$, I think I ...
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### Need Help With First Order Intuitionistic Tableaux

I have a question about semantic tableaux for Intuitionistic FOL. I’ll post a sample tableaux that I’m pretty sure I’m doing wrong, and then I’ll post a sequent calculus approach to show where I get ...
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### Is intuitionist logic two-valued?

On this page https://en.wikipedia.org/wiki/Principle_of_bivalence : Intuitionistic logic is a two-valued logic but the law of excluded middle does not hold. On this page https://en.wikipedia.org/...
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### How is the “ Axiom of choice is trivial in intuitionistic logic”?

In slide 28 of these slides, the author claims that the “Axiom of choice is trivial in intuitionistic logic” and that classical logic makes it a “ monster from outer space”. How is it trivial when it’...
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### Is there a non-constructive proof-functional logic

I understand that classical logic preserves truth, is bivalent, and contains non-constructive proofs. In contrast, intuitionistic logic preserves justification/verification for a proof, is not ...
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