Definition:Intuitionistic Propositional Logic
The intuitionist school of mathematics is one which adopts the following philosophical position:
- "Although we may know that it is not the case that a statement $p$ is (provably) false, we don't necessarily know that it is (provably) true either."
Thus the intuitionist school rejects the Law of the Excluded Middle.
The classical school, by affirming that if a statement is not true it must be false, and if it is not false it must be true, accepts as an axiom that "not not-true" must mean "true".
Also known as
Some prefer to address this logic by its practitioners, calling it intuitionist (propositional) logic.
This field of logic is also (more intuitively) (no pun intended) known as constructive logic or constructivist logic.
- 1993: M. Ben-Ari: Mathematical Logic for Computer Science (1st ed.) ... (previous) ... (next): $\S 1.4$: Non-standard logics
- 2000: Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems ... (previous) ... (next): $\S 1.2.5$: An aside: proof by contradiction