Nonmonotonic logics
Monotonicity:
If a conclusion ? is a consequence of a set of premises S, and S’ is a set of sentences containing S, then ? is a consequence of S’.
Formally: if S ? S’, then Cons(S) ? Cons(S’)
Standard logics are monotonic.
E.g., propositional logic, first-order predicate logic, standard modal logics
Since the 80s, there has been a burst of research on nonmonotonic logics