1993 Volume 4 Issue 1 Pages 1-8
Grouping of strata is one of the most fundamental works in geological studies. The grouping is mathematically formulated as the work to define an equivalence relation D on a set of strata B. The equivalence relation D constructs a quotient set B/D, and each group of strata corresponds to an equivalence class relative to the equivalence relation D. The grouping of strata introduces the problem how we should define relations on B/D from relations given on the original set B. As a logical approach to such a problem, this paper discusses how to define the time relation K′ on a quotient set B/D, based on Shiono and Wadatsumi (1991) 's formulation of a relation K on set B of strata such that aKb if and only if a stratum a is older than a stratum b. It is concluded that the relation K′ on B/D can be derived from the relation K given on B in such a manner that [a] K′ [b] if and only if xKy for every x ∈ [a] and y ∈ [b], where [a] and [b] are any equivalence classes in B/D, and then the relation K′∪E′ on B/D is also a partial ordering if the relation K∪E is a partial ordering.
