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Nonmonotonic reasoning on a constructive time structure

The author introduces a temporal logic called interval division logic, IDL, based on the constructive temporal ontology. In IDL, time is regarded as a constructive object which is built from an interval by iterating the interval division every time a new temporal fact is recognized. IDL as a sound and complete logical system which is as expressive as the Buich tree automata. In order to examine how the persistence problem is treated on this ontology, the author extends a nonmonotonic version of IDL based on the model preference in which any belief is changed as late as possible in the epistemological order rather than the temporal order. The Yale shooting problem is discussed in this framework.