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.

Read more about this topic:  Classical Logic

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