Need help in defining

We use formula Occurs(a, t, D(t)) to denote that an atomic process occurs with respect to time t with a duration of D(t).
Axiom1. Occurs(a, t, D(t)) implies D(t) ≥ 0 & for all t1(In(t1, t) implies there exists t2(Part(t2, t1) & Occurs(a, t2)))
N.B. Axiom 1 applies to divisible intervals, non-divisible moments, and points.

Definition: A business process p is defined as a pair (A , R(A)) where
1. A = {Occurs(p1, t1, D(t1)), …, Occurs(pn, tn, D(tn))}
2. R(A) = {Relation(ti, tj) | 1 ≤ i, j ≤ n}
Specially, an atomic process can be taken as a special business process, since for any atomic process a, R({a}) = Null set
For a R(A), we use DR(A) to denote the deduced temporal constraint which contains all the relations of R(A), plus all the other relations that can be deduced from R(A). ----- A formal definition of this, and some examples???????????????????

Definition: Business process (A1, R(A1)) is called a sub-process of business process (A2, R(A2)) if and only if:
1. A1 subset of A2
2. DR(A1) subset of DR(A2).