Intuitionistic logic - Wikipedia, the free encyclopedia - The Diigo Meta page

• 07 Oct 14
  

  Joao Pita Costa
  • to recognize valid formulas, it is sufficient to consider a single Heyting algebra whose elements are the open subsets of the real line R.^[4] In this algebra, the ∧ and ∨ operations correspond to set intersection and union, and the value assigned to a formula A → B is int(A^C ∪ B), the interior of the union of the value of B and the complement of the value of A. The bottom element is the empty set ∅, and the top element is the entire line R. The negation ¬A of a formula A is (as usual) defined to be A → ∅. The value of ¬A then reduces to int(A^C), the interior of the complement of the value of A, also known as the exterior of A. With these assignments, intuitionistically valid formulas are precisely those that are assigned the value of the entire line.^[4]
• 23 Feb 14
  

  James Nicholls

  Imported From Firefox OLD Studies 2004-2011 MATHS

• 26 Jul 13
  

  Dante-Gabryell Monson

  "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."

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• 06 Nov 12
  

  Francisco Gomes

  philosophy mathematics intuitionisc logic classical

• 03 Aug 11
  

  wolf hesse

  math phil logic

• 08 Apr 11
  

  Julio B

  logica logic

• 15 Nov 10
  

  lbjrebecca

  • what it means for a statement to be true. In classical logic, all well-formed statements are assumed to be either true or false, even if we do not have a proof of either. In constructive logic, a statement is only true if there is a proof that it is true, and only false if there is a proof that it is false. Operations in constructive logic preserve justification, rather than truth. Syntactically, intuitionist logic differs from classical logic in that the law of excluded middle and double negation elimination are not axioms of the system, and cannot be proved in it.

     
• 02 Sep 10
  

  logic philosophy mathematics intuitionistic learning theory wikipedia

• 21 Nov 09
  

  Călin Ardelean

  logic science article

• 07 Apr 07
  

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