Philosopher Susan Haack uses the term "deviant logic" to describe certain non-classical systems of logic. In these logics,
- the set of well-formed formulas generated equals the set of well-formed formulas generated by classical logic.
- the set of theorems generated is different from the set of theorems generated by classical logic.
The set of theorems of a deviant logic can differ in any possible way from classical logic's set of theorems: as a proper subset, superset, or fully exclusive set. A notable example of this is the trivalent logic developed by Polish logician and mathematician Jan Łukasiewicz. Under this system, any theorem necessarily dependent on classical logic's principle of bivalence would fail to be valid. The term first appears in Chapter 6 of W.V.O. Quine's Philosophy of Logic, New Jersey: Prentice Hall (1970), which is cited by Haack on p.15 of her book.
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... stand well the test of time, particularly with the "extraordinary proliferation of nonclassical logics in the past two decades—paraconsistent logics, linear logics, substructural logics ...
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