A system of logic with the property that adding premises to a system can cause a proposition to become invalidated--in other words, additional information can cause a belief that was previously true to become false. In classical FirstOrderLogic, the rule "once true, always true" holds--if a statement is true (explicitly so, or inferrable from the axioms in the system), then addition of additional facts or axioms cannot make it false. (Additional rules/axioms can make the system inconsistent; but that's another kettle of fish). In systems with the ClosedWorldAssumption (where falsehood is the absence of truth), things can go from false to true. In systems with the OpenWorldAssumption (where falsehood must be stated explicitly), things can go from unknown to either true or false; but things that are known (true/false) can neither become unknown or take the opposite known state.
In NonMonotonicLogic, this rule vanishes; additional information can falsify statements that were held to be true.
Work in this area has been JohnMcCarthy's primary focus at Stanford for the last few decades.