Global Set Theory, Edition 2

Binary logic, representing relations between true (1) and false (0), corresponds to Boolean lattice, and called classical logic, where lattice is an ordered set with operations \(\vee\) and \(\wedge\). Classical logic has the law of excluded middle and distributive law.

Intuitionistic logic drops the law of excluded middle of classical logic, while quantum logic replaces the full distributive law of classical logic by weaker distributivity.

Global logic has a logical operation which represents the lattice oder. We called it basic implication. Introduction of the basic implication enables us to express various logic and various set theory, such as quantum logic and quantum set theory.