# intuitionistic logic

## English

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### Noun

1. (mathematics, logic) A type of logic which rejects the axiom law of excluded middle or, equivalently, the law of double negation and/or Peirce's law. It is the foundation of intuitionism.
Just because $P \vee \neg P$ is not axiomatically true (for all P) does not mean that $\neg(P \vee \neg P)$ is true (for some P); this would lead to the contradiction $\neg P \wedge \neg \neg P$. In fact, the deduction $\neg \forall P : (P \vee \neg P) \Rightarrow \exists P : \neg (P \vee \neg P)$ is not valid in second-order intuitionistic logic.
Whereas classical logic and also ternary logic have truth valuation functions for assertions and can use truth tables to evaluate tautologies, intuitionistic logic has no truth-value functions and cannot use truth tables to evaluate tautologies (instead, Kripke models may be used).
The Lindenbaum-Tarski algebra of propositional intuitionistic logic is a Heyting algebra.[1]
One reason why intuitionistic logic doesn't have any specific truth-valuation functions might be because intuitionistic logic can be concretized into a variety of different specific logics, each one with its own Heyting-algebra and truth-valuation functions.