Non-classical logic
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Non-classical logics (and sometimes alternative logics) is the name given to formal systems which differ in a significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is done, including by way of extensions, deviations, and variations. The aim of these departures is to make it possible to construct different models of logical consequence and logical truth.
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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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