Abstract
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 :
[A1] W∪W-1∪E=I, [A2] L⊂W and [A3] C⊂K.
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.
The present study suggests a possibility that we can systematize our geologic knowledge in a formal system based on several axioms.
