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- Intuitionistic_logic abstract "Intuitionistic logic, sometimes more generally called constructive logic, is a system of symbolic logic that differs from classical logic by replacing the traditional concept of truth with the concept of constructive provability. For example, in classical logic, propositional formulae are always assigned a truth value from the two element set of trivial propositions ("true" and "false" respectively) regardless of whether we have direct evidence for either case. In contrast, propositional formulae in intuitionistic logic are not assigned any definite truth value at all and instead only considered "true" when we have direct evidence, hence proof. (We can also say, instead of the propositional formula being "true" due to direct evidence, that it is inhabited by a proof in the Curry-Howard sense.) Operations in intuitionistic logic therefore preserve justification, with respect to evidence and provability, rather than truth-valuation. A consequence of this point of view is that intuitionistic logic is not a two-valued logic, nor even a finite-valued logic, in the familiar sense: although intuitionistic logic retains the trivial propositions from classical logic, each proof of a propositional formula is considered a valid propositional value, thus by Heyting's notion of propositions-as-sets, propositional formulae are (potentially non-finite) sets of their proofs.Semantically, intuitionistic logic is a restriction of classical logic in which the law of excluded middle and double negation elimination are not admitted as axioms. Excluded middle and double negation elimination can still be proved for some propositions on a case by case basis, however, but do not hold universally as they do with classical logic.Several semantics for intuitionistic logic have been studied. One semantics mirrors classical Boolean-valued semantics but uses Heyting algebras in place of Boolean algebras. Another semantics uses Kripke models.Intuitionistic logic is practically useful because its restrictions produce proofs that have the existence property, making it also suitable for other forms of mathematical constructivism. Informally, this means that if you have a constructive proof that an object exists, you can turn that constructive proof into an algorithm for generating an example of it.Formalized intuitionistic logic was originally developed by Arend Heyting to provide a formal basis for Brouwer's programme of intuitionism.".
- Intuitionistic_logic thumbnail Rieger-Nishimura.svg?width=300.
- Intuitionistic_logic wikiPageExternalLink naclp89.ps.
- Intuitionistic_logic wikiPageExternalLink j.jal.2004.07.016.
- Intuitionistic_logic wikiPageExternalLink logic-intuitionistic.
- Intuitionistic_logic wikiPageExternalLink index.php.
- Intuitionistic_logic wikiPageExternalLink ESSLLI'05.pdf.
- Intuitionistic_logic wikiPageExternalLink troelstra.pdf.
- Intuitionistic_logic wikiPageExternalLink Blackwell(Dalen).pdf.
- Intuitionistic_logic wikiPageExternalLink mezhirovs-game-for-ipc.
- Intuitionistic_logic wikiPageExternalLink validity-tester-for-ipc.
- Intuitionistic_logic wikiPageExternalLink kripke_intuitionism.pdf.
- Intuitionistic_logic wikiPageID "169262".
- Intuitionistic_logic wikiPageRevisionID "603182419".
- Intuitionistic_logic hasPhotoCollection Intuitionistic_logic.
- Intuitionistic_logic subject Category:Constructivism_(mathematics).
- Intuitionistic_logic subject Category:Intuitionism.
- Intuitionistic_logic subject Category:Logic_in_computer_science.
- Intuitionistic_logic subject Category:Non-classical_logic.
- Intuitionistic_logic subject Category:Systems_of_formal_logic.
- Intuitionistic_logic type Ability105616246.
- Intuitionistic_logic type Abstraction100002137.
- Intuitionistic_logic type Cognition100023271.
- Intuitionistic_logic type Know-how105616786.
- Intuitionistic_logic type Logic105664069.
- Intuitionistic_logic type Method105660268.
- Intuitionistic_logic type PsychologicalFeature100023100.
- Intuitionistic_logic type System105661996.
- Intuitionistic_logic type SystemsOfFormalLogic.
- Intuitionistic_logic comment "Intuitionistic logic, sometimes more generally called constructive logic, is a system of symbolic logic that differs from classical logic by replacing the traditional concept of truth with the concept of constructive provability. For example, in classical logic, propositional formulae are always assigned a truth value from the two element set of trivial propositions ("true" and "false" respectively) regardless of whether we have direct evidence for either case.".
- Intuitionistic_logic label "Intuitionismus".
- Intuitionistic_logic label "Intuitionistic logic".
- Intuitionistic_logic label "Intuïtionisme".
- Intuitionistic_logic label "Logica intuizionista".
- Intuitionistic_logic label "Logika intuicjonistyczna".
- Intuitionistic_logic label "Logique intuitionniste".
- Intuitionistic_logic label "Lógica intuicionista".
- Intuitionistic_logic label "Lógica intuicionista".
- Intuitionistic_logic label "Интуиционистское исчисление высказываний".
- Intuitionistic_logic label "直観論理".
- Intuitionistic_logic label "直觉主义逻辑".
- Intuitionistic_logic sameAs Intuicionistická_logika.
- Intuitionistic_logic sameAs Intuitionismus.
- Intuitionistic_logic sameAs Lógica_intuicionista.
- Intuitionistic_logic sameAs Logique_intuitionniste.
- Intuitionistic_logic sameAs Logica_intuizionista.
- Intuitionistic_logic sameAs 直観論理.
- Intuitionistic_logic sameAs Intuïtionisme.
- Intuitionistic_logic sameAs Logika_intuicjonistyczna.
- Intuitionistic_logic sameAs Lógica_intuicionista.
- Intuitionistic_logic sameAs m.016p04.
- Intuitionistic_logic sameAs Q176786.
- Intuitionistic_logic sameAs Q176786.
- Intuitionistic_logic sameAs Intuitionistic_logic.
- Intuitionistic_logic wasDerivedFrom Intuitionistic_logic?oldid=603182419.
- Intuitionistic_logic depiction Rieger-Nishimura.svg.
- Intuitionistic_logic isPrimaryTopicOf Intuitionistic_logic.