Nonmonotonic Reasoning Systems
A way to overcome the situation described in the example is the use of beliefs (or assumptions), i.e. hypothetical assertions on the domain, which are not completely supported by evidence, but are not in contrast with what is already known.
From a belief, we can derive new facts in a normal way, but, if a contradiction arises, we have to be able to retract it, and to perform all the adequate bookkeeping needed.
A reasoning system based on beliefs and able to manage contradictions is called nonmonotonic.
TMS are practical example of nonmonotonic systems.