Non-classical logic
FORMAL SYSTEMS OF LOGIC THAT SIGNIFICANTLY DIFFER FROM STANDARD LOGICAL SYSTEMS
Non-Aristotelian logic; Nonclassical logic; Alternative logic
Non-classical logics (and sometimes alternative logics) are formal systems that 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.