Human abilities in the common sense informatic situation also include what may be called elaboration tolerance--the ability to elaborate a statement of some facts without having to start all over. Thus when we begin to think about a problem, e.g. determining the height of a building, we form a bounded context and try to solve the problem within it. However, at any time more facts can be added, e.g. about the precision with which the time for the barometer to fall can be estimated using a stop watch and also the possibilities of acquiring a stop watch.
Elaboration Tolerance discusses about 25 elaborations of the Missionaries and Cannibals problem.
What I have so far said so far about approximate concepts, nonmonotonic reasoning and elaboration tolerance is independent of whether mathematical logic, human language or some other formalism is used.
In my opinion, the best AI results so far have been obtained using and extending mathematical logic.