Intuitonistic Basis for Non-Monotonic Logic

In other words whatever can be obtained from assumption A can still be obtained if we add to A more assumptions. In many cases, reasoning is non-monotonic. Consider the story below of the World-Trave-Agency (WTA). The story shall serve as the basis for introducing a system of non-monotonic logic. WTA offers package tours from New York to Paris and Stuttgart. Every Sunday, a group of New Yorkers board a WTA plane in Now York, some get off at Paris and the rest continue to Stuttgart. The Stuttgart office arranges for hotels and tours in Europe. Our non-monotonic reasoning will be done by the the Stuttgart office. At 12:00 Stuttgart time, 3 hours after the scheduled New York take-off of the WTA group, the Stuttgart office learns that a terrorist attack was launched at Paris Airport, 2 planes were hijacked and that all flights nearing France are rerouted. Stuttgart has to decide what to do with the WTA-group. All telephone lines to New York are busy. The only established fact is that the WTA-plane did take off (some passenger’s wife happened to leave a message). Stuttgart reasons that in this case the WTA-plane will be rerouted to London, the Paris passengers will stay in London and the Stuttgart passengers will arrive tonight. This reasoning is performed on the basis of knowledge of WTA procedures and connections.