I Value of intuitionistic logic

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Thread starter cianfa72
Start date Yesterday, 8:58 AM
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Intuition Predicate logic Proof by contradiction Propositional logic Theorem

Yesterday, 8:58 AM

cianfa72

TL;DR Summary: About the value and significance of intuitionistic logic in modeling some kind of worlds.

I'm taking a look at intuitionistic propositional logic (IPL). Basically it exclude Double Negation Elimination (DNE) from the set of axiom schemas replacing it with Ex falso quodlibet: ⊥ → p for any proposition p (including both atomic and composite propositions).

In IPL, for instance, the Law of Excluded Middle (LEM) p ∨ ¬p is no longer a theorem.

My question: aside from the logic formal perspective, is IPL supposed to model/address some specific "kind of world" ?

Thanks.

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...

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