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 deviant logic first appears in Chapter 6 of Willard Van Orman Quine's Philosophy of Logic, New Jersey: Prentice Hall (1970), which is cited by Haack on p. 15 of her book.
In such systems, any novel theorem would not parse in classical logic due to modal operators.
He concedes however that "as a defense of a philosophical position, Deviant Logic retains its significance."