Deviant logic is atype of logic incompatible withclassical logic. PhilosopherSusan Haack[1] uses the termdeviant logic to describe certainnon-classicalsystems of logic. In these logics:
The set of theorems of a deviant logic can differ in any possible way from classical logic's set of theorems: as a propersubset, superset, or fully exclusive set. A notable example of this is thetrivalent logic developed byPolishlogician andmathematicianJan Łukasiewicz. Under this system, any theorem necessarily dependent on classical logic'sprinciple of bivalence would fail to be valid. The termdeviant logic first appears in Chapter 6 ofWillard Van Orman Quine'sPhilosophy of Logic, New Jersey: Prentice Hall (1970), which is cited by Haack on p. 15 of her book.
Haack also described what she calls aquasi-deviant logic. These logics are different from pure deviant logics in that:
Finally, Haack defined a class of merelyextended logics. In these,
Some systems ofmodal logic meet this definition. In such systems, any novel theorem would not parse in classical logic due to modal operators. While deviant and quasi-deviant logics are typically proposed as rivals to classical logic, the impetus behind extended logics is normally only to provide a supplement to it.
Achille Varzi in his review[2] of the 1996 edition of Haack's book writes that the survey did not 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,nonmonotonic logics, innumerable other logics for AI and computer science." He also finds that Haack's account ofvagueness "is now seriously defective." He concedes however that "as a defense of a philosophical position,Deviant Logic retains its significance."
{{cite book}}: CS1 maint: publisher location (link) (First appeared in 1974 asDeviant Logic, published by Cambridge University Press. The 1996 edition includes some additional essays published between 1973 and 1980, particularly onfuzzy logic.)