時間的推論のための構成的論理IDL

抄録

In this paper, we introduce 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 in the process of temporal reasoning. Namely, every time an unknown (past, present or future) event is recognized, the current time structure is modified by dividing its corresponding interval into two intervals before and after that event, so that the time structure of IDL has a form of binary tree of which leaves constitute the current sequence of events. Although IDL itself is a sound and complete logical system which is as expressive as the Buich infinite tree automata, we extend IDL into a nonmonotonic version based on the model preference method in order to examine how the persistence problem is treated on this constructive ontology. Since the persistence itself is due to the retention of the belief rather than the inertia of real world, the interpretation for a sequence of events depends not only on the temporal order of the events but also on the epistemological order in which each event in the sequence is recognized. Therefore, we use the order of temporal inference rather than the temporal order for the model minimization. Temporal prediction and nondeterministic event problems are discussed in this framework.