There are many kinds of non-classical logic, which include: •
Computability logic is a semantically constructed formal theory of computability—as opposed to classical logic, which is a formal theory of truth—that integrates and extends classical, linear and intuitionistic logics. •
Dialectical logic is the system of laws of thought, developed within the
Hegelian and
Marxist traditions, which seeks to supplement or replace the laws of
formal logic. The precise nature of the relation between dialectical and formal logic was hotly debated within the Soviet Union and China. •
Dynamic semantics interprets formulas as update functions, opening the door to a variety of nonclassical behaviours •
Many-valued logic rejects bivalence, allowing for
truth values other than true and false. The most popular forms are
three-valued logic, as initially developed by
Jan Łukasiewicz, and infinitely-valued logics such as
fuzzy logic, which permit any real number between 0 and 1 as a truth value. •
Intuitionistic logic rejects the
law of the excluded middle,
double negation elimination, and part of
De Morgan's laws; •
Linear logic rejects
idempotency of
entailment as well; •
Paraconsistent logic (e.g.,
relevance logic) rejects the
principle of explosion, and has a close relation to
dialetheism; •
Quantum logic •
Relevance logic,
linear logic, and
non-monotonic logic reject monotonicity of entailment; •
Non-reflexive logic (also known as
"Schrödinger logics") rejects or restricts the
law of identity; == Classification of non-classical logics according to specific authors ==