Modeling and inference of extended interval temporal logic for nondeterministic intervals

Extended interval temporal logic (EITL), an extension of the traditional point-interval temporal logic (PITL), is proposed. In contrast to PITL that represents the dynamic aspects of deterministic intervals, EITL can model and reason about the temporal relations among nondeterministic intervals in discrete-event systems, in which the duration of an event is indeterminate and only the lower bound and upper bound of the ending time can be predicted in advance. Time Petri nets (TPNs) are used for modeling EITL, for they give a straightforward view of temporal relations between the extended intervals and also provide a number of theoretical and practical analysis methods. An inference engine based on the TPN modeling complemented with algebraic inequalities is proposed to construct an analytical representation of the EITL relations and solve qualitative temporal reasoning problems. Linear inference mechanism based on TPN reduction rules is used to infer new temporal relations and handle quantitative temporal reasoning problems with linear time complexity, as our example shows.