**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;

While not entailed by the preceding conditions, contemporary discussions of classical logic normally only include propositional and first-order logics.

The intended semantics of classical logic is bivalent. With the advent of algebraic logic it became apparent however that classical propositional calculus admits other semantics. In Boolean-valued semantics (for classical propositional logic), the truth values are the elements of an arbitrary Boolean algebra; "true" corresponds to the maximal element of the algebra, and "false" corresponds to the minimal element. Intermediate elements of the algebra correspond to truth values other than "true" and "false". The principle of bivalence holds only when the Boolean algebra is taken to be the two-element algebra, which has no intermediate elements.

Read more about Classical Logic: Examples of Classical Logics, Non-classical Logics

### Famous quotes containing the words classical and/or logic:

“Culture is a sham if it is only a sort of Gothic front put on an iron building—like Tower Bridge—or a *classical* front put on a steel frame—like the Daily Telegraph building in Fleet Street. Culture, if it is to be a real thing and a holy thing, must be the product of what we actually do for a living—not something added, like sugar on a pill.”

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“There is no morality by instinct.... There is no social salvation—in the end—without taking thought; without mastery of *logic* and application of *logic* to human experience.”

—Katharine Fullerton Gerould (1879–1944)