Classical Logic - Non-classical Logics

Non-classical Logics

• Computability logic is a semantically constructed formal theory of computability, as opposed to classical logic, which is a formal theory of truth; integrates and extends classical, linear and intuitionistic logics.
• Many-valued logic, including fuzzy logic, which rejects the law of the excluded middle and allows as a truth value any real number between 0 and 1.
• Intuitionistic logic rejects the law of the excluded middle, double negative elimination, and the De Morgan's laws;
• Linear logic rejects idempotency of entailment as well;
• Modal logic extends classical logic with non-truth-functional ("modal") operators.
• Paraconsistent logic (e.g., dialetheism and relevance logic) rejects the law of noncontradiction;
• Relevance logic, linear logic, and non-monotonic logic reject monotonicity of entailment;

In Deviant Logic, Fuzzy Logic: Beyond the Formalism, Susan Haack divided non-classical logics into deviant, quasi-deviant, and extended logics.