Preliminary Study on Axiom System Related to the Law of Superposition

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  • SHIONO Kiyoji
    Department of Geosciences, Faculty of Science, Osaka City University
  • WADATSUMI Kiyoshi
    Department of Geosciences, Faculty of Science, Osaka City University

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  • 地層累重の法則に関連する公理系の試案

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The present paper discusses a logical structure of geologic knowledge related to the laws of superposition, original horizontality and original lateral continuity, based on mathematical formulation. First we define several geologic relations between two strata; i.e. binary relations on set B of strata, based on a function f from a subset Ω of the real space into set B. Next we discuss what are derived from three axioms :<BR>[A1] W∪W-1∪E=I, [A2] L⊂W and [A3] C⊂K.<BR>The axiom A1 provides a logical basis for geologists to infer spatial relations between strata from observation of exposed strata. The axiom A2 generates the ordering structure in set B which is called the stratigraphic sequence, and the axiom A3 introduces a historical view into geology. Further from a set of three axioms, we can deduce a validity of the geologic method to infer the formative order of strata from field works.<BR>The present study suggests a possibility that we can systematize our geologic knowledge in a formal system based on several axioms.

Journal

  • Geoinformatics

    Geoinformatics 3 (4), 203-210, 1992

    Japan Society of Geoinformatics

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