Classical Logic

Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. The class is sometimes called standard logic as well. They are characterised by a number of properties:

• Law of the excluded middle and double negative elimination;
• Law of noncontradiction, and the principle of explosion;
• Monotonicity of entailment and idempotency of entailment;
• Commutativity of conjunction;
• de Morgan duality: every logical operator is dual to another.

de Morgan duality is the duality between logical operators as shown in the table below:

The first two operators in each column exist in both intuitionistic and dual-intuitionistic propositional logic and the last two in each column exist in both forms of predicate logic and modal logic (respectively), but they are still dual as shown. All of these exist in classical logic (although some of the paraconsistent operators are not widely used), and the two forms of negation (¬\neg and −-) are the same there.