Classical logic Glossary
Definition
"Classical" logic, also called "orthodox" logic in these notes, is the standard account of reasoning, based on truth-functional (boolean) connectives and the quantifiers all and some. It contrasts with constructive logic, which is based on a different notion of truth, fuzzy logic, for which truth values have a non-boolean form, and relevant logic, which takes a different attitude to derivations and proof.
Comments
Classical logic was developed by Boole Boole and Frege Frege in the 19th century, with important early work also by Russell Russell and others at the start of the 20th century. It replaced the earlier logic (previously thought of as "classical") which was mainly a theory of syllogistic reasoning, deriving originally from ancient work by Aristotle.
Free logic is sometimes classified as a non-classical logic, but is better seen as a variant of the classical paradigm because it retains the classical view of truth and inference but just extends it to allow for partial functions. Modal logic (not really treated in these notes) is also best regarded as an extension of classical logic rather than as an alternative to it.