Definition from Wiktionary, the free dictionary
- (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 is not axiomatically true (for all P) does not mean that is true (for some P); this would lead to the contradiction . In fact, the deduction 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.
- 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.