In the previous paper (Shiono and Yamaguchi, 2022), we have shown that the time range of species can be expressed in a form of unions of short time intervals created by partitioning the time range T of a taxon Σ at the appearance times and the extinction times of species in Σ, and that set operations of time ranges of species can be performed consistently as discrete processing of the short time intervals over the set T_M whose elements are an empty set, single short time intervals and unions of short time intervals. The present paper discusses the mathematical structure of operations over the set T_M from a viewpoint of Boolean algebra. The results are summarized as follows: (i) T_M is a Boolean algebra with a zero element ∅ and a unity T, (ⅱ) the Boolean algebra T_M is isomorphic to Bⁿ, or the direct product of n identical sets B = {0, 1} if T is divided into n short intervals, and (ⅲ) using the isomorphism from Bⁿ to T_M, set operations over T_M can be transformed into calculations of n-tuples, or elements of Bⁿ, which are suitable for computer processing.

The Shoji’s papers in the geoinformatics field are briefly reviewed here on the occasion that he was awarded by Japan Society of Geoinformatics. The topics are structural analysis using Wulff net, zoning and mineralization sequence from spatiotemporal point of view, and the prize-penalty function, the information-cost function, and the cell entropy for optimizing geoscience survey.