Examples of Non-classical Logics
- Fuzzy logic 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;
- 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.
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