# Definitions for intuitionistic logicin·tu·ition·is·tic log·ic

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1. intuitionistic logicnoun

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.

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1. Intuitionistic logic

Intuitionistic logic, or constructive logic, is a symbolic logic system that differs from classical logic in its definition of 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 "true" only if there is a constructive proof that it is true, and "false" only if there is a constructive proof that it is false. Operations in constructive logic preserve justification, rather than truth. Syntactically, intuitionistic logic is a restriction of classical logic in which the law of excluded middle and double negation elimination are not axioms of the system, and cannot be proved. There are several semantics commonly employed. One semantics mirrors classical Boolean-valued semantics but uses Heyting algebras in place of Boolean algebras. Another semantics uses Kripke models. Constructive 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.

### Numerology

1. Chaldean Numerology

The numerical value of intuitionistic logic in Chaldean Numerology is: 9

2. Pythagorean Numerology

The numerical value of intuitionistic logic in Pythagorean Numerology is: 3

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"intuitionistic logic." Definitions.net. STANDS4 LLC, 2023. Web. 23 Mar. 2023. <https://www.definitions.net/definition/intuitionistic+logic>.

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