Abstract: Temporal span is one of the most important objects for temporal assertion. How to compute the result of the operation between temporal spans accurately is the key issue. Since temporal span is uncanonical and can be affected by the flexible temporal granularity, the granularity conversion is not always effective. By vectorizing process, the temporal granularity system can be isomorphism with the n dimensional vector space. Furthermore, temporal span can be mapped to free vector in the vector space after being completed and smoothed. Thus, the operations of temporal spans in any complex situations can be simplified with the operation rule in the vector space.

Key words: Vectorizing processing, Temporal spans, Completed processing, Smoothed processing, hemporal granularity svstem