# nLab classical logic

Classical logic is the form of logic usually accepted as standard and traced back (at least) to Aristotle. The particular features that distinguish classical logic are (perhaps not a complete list):

• a distributive lattice of logical operations ($\wedge$ and $\vee$);
• the structural rules of weakening, contraction, and (where meaningful) exchange;
• an involutory negation.

In contrast, minimal, intuitionistic, and (some forms of) paraconsistent logics have the distributive lattice and the structural rules but no involutory negation. On the other hand, linear logic and (other forms of) paraconsistent logic have the distributive lattice and the involutory negation but lack some structural rules. Then again, quantum logic and (yet other forms of) paraconsistent logic have the structural rules and the involutory negation but lack the distributive lattice.

In category theory (and in the foundations of mathematics generally), intuitionistic logic is most often contrasted to classical logic; the difference is given by the law of excluded middle, which holds classically but not intuitionistically.

Revised on January 12, 2015 20:52:18 by Zoran Škoda (109.227.20.138)