The Inference Engine of Extended Interval Temporal Logic

Extended interval temporal logic(EITL) can model and reason about the temporal relations between nondeterministic intervals in discrete event systems where the duration of an action or event is indeterminate or unpredictable and only the low bound and up bound of the terminal time can be predicted. Generally, the temporal logic relations among extended intervals are described by a group of statements. Every statement states the temporal logic relations between two intervals. A new inference engine for EITL is proposed in this paper, and with this inference engine, unknown temporal relations among the extended temporal intervals can be inferred from the known ones. Some former methods of inferring unknown temporal relations are only based on the rules of inequation, while this new engine is based on both the rules of inequation and Time Petri Nets(TPN). This engine has four steps: 1) constructing TPN model of the known temporal relations; 2) simplifying the TPN model; 3) computing the inequation; 4) transforming the inequation into extended temporal logic relation. TPN models have been shown to be effective for describing concurrent, parallel, nondeterministc, and synchronous behaviors. Furthermore, there is a well developed mathematics theory for analyzing the systems. With TPN, the specifications of a system given by temporal statements can be transformed into a representation of graph, and the analysis techniques of TPN can be used for model solution. The new inference engine provides a powerful tool for analyzing complicated temporal relations qualitatively, and the inferring results may be not unique. It theoretically constructs an analytical representation of the temporal relations between appointed extended temporal intervals with the help of known relations among several intervals. In a sense, this methodology is an extension, as well as the supplementary, of the quantitative analyzing method on determining the temporal relations of extended temporal intervals. So the inferring process can be simplified and the inferring result is unique if some specific numerical values are provided.