Online ISSN : 1347-541X
Print ISSN : 0388-502X
ISSN-L : 0388-502X
Current issue
Displaying 1-7 of 7 articles from this issue
Cover (GEOINFORMATICS 2023 Vol34. No.1)
  • Kiyoji SHIONO, Kumiko YAMAGUCHI
    Article type: Article
    2023 Volume 34 Issue 1 Pages 3-11
    Published: March 25, 2023
    Released on J-STAGE: March 25, 2023

    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 TM 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 TM from a viewpoint of Boolean algebra. The results are summarized as follows: (i) TM is a Boolean algebra with a zero element ∅ and a unity T, (ⅱ) the Boolean algebra TM 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 TM, set operations over TM can be transformed into calculations of n-tuples, or elements of Bn, which are suitable for computer processing.

    Download PDF (1457K)
Instructions to Contributors
Manuscript Submission Form, Guaranty, Membership Application Form, Editorial note