Axiom System for Cards on a Table as a Logical Model of Strata Bearing Fossils

SHIONO Kiyoji

doi:10.6010/geoinformatics1990.8.4_257

In order to develop efficient algorithms for computer processing of geological data, we need to establish a mathematical framework which integrates a variety of geological methods. This paper presents a mathematical model composed of three sets B, Z and F whose members are cards, numbers and symbols, respectively, relations between sets and several axioms. This is a preliminary study to formulate a fundamental framework of biostratigraphic methods constructed on the basic principles of geology; the law of original horizontality, the law of original lateral continuity, the law of superposition and the law of faunal succession. In addition to three axioms A₁, A₂ and A₃ similar to those which Shiono and Wadatsumi (1992) proposed as properties of layering strata, an axiom A₄ is assumed to introduce a property of fossils or the law of faunal succession into the theoretical system.<BR>It is confirmed that A₁, A₂ and A₃ are formally equivalent to Shiono and Wadatsumi (1992) 's axioms through a fact that they provide similar theorems.From A₄, we derived several inference rules on order relations between cards and/or groups of cards, which are interpreted to formulate biostratigraphic procedures.Further, we obtained an important result that if A₁, A₂, A₃ and A₄ hold true on B, then properties equivalent to A₁, A₂ and A₃ hold true also on a quotient set B/D, where D is an equivalence relation such that aDb iff a and b are marked with the same symbol.Thus the present model, in spite of its simplicity, reflects fundamental properties of strata baring fossils and provides a clue to systematize mathematical bases of biostratigraphy.

Axiom System for Cards on a Table as a Logical Model of Strata Bearing Fossils

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