Definition
A superintuitionistic logic is a set L of propositional formulas in a countable set of variables pi satisfying the following properties:
- all axioms of intuitionistic logic belong to L;
- if F and G are formulas such that F and F → G both belong to L, then G also belongs to L (closure under modus ponens);
- if F(p1, p2, ..., pn) is a formula of L, and G1, G2, ..., Gn are any formulas, then F(G1, G2, ..., Gn) belongs to L (closure under substitution).
Such a logic is intermediate if furthermore
- L is not the set of all formulas.
Read more about this topic: Intermediate Logic
Famous quotes containing the word definition:
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)