Clear and Vague Rules
In most real-life cases, the child Variable is not completely determined by its parents. In fact in many projects we only have the roughest of ideas how much of a contribution our intervention can really make, and it may not be very big.
So we can say a Rule is “complete” if it more or less totally determines the Levels of the parent Variables, “slight” if there is only just a discernible connection and “incomplete” otherwise.
Family spending power !Rule:incomplete (Influence=-)Income (Influence=-)Debts (Influence=+)Savings
The circle which follows the arrow it shows roughly how much of an influence the parent Variable(s) have. In this case, the half-filled circle, which is also the default, shows we think there is some noteworthy influence but not total control.
What is perhaps surprising here is that we can apply the same idea of (in)completeness to Rules within Definitions as well as Theories, giving us a new insight into the nature of some problems with incomplete Definitions too, see xx.
Expressing the completeness of Rules using full, half-full and empty circles
But it is also possible that there is just barely a connection - the consequence just about responds to the best efforts of the Influences. In the next example, even though the influence is marked as only slight, it would be a world sensation: homoeopathic medicine has some effect on human health.
Health !Rule:slight ((lo-hi)) Homoeopathic intervention ((no,yes))
The empty circle says merely that there is some connection, however weak.
And below is the obviously false claim that an individual’s behaviour is totally determined by their genetic make-up - the filled circle is a convention to show that the Consequence is supposed to be totally determined by the Influence(s).
Human individual's behaviour !Rule:complete ((lo-hi)) Individual's genetic make-up ((no,yes))
In the specification of a Rule, the signs
!Rule:complete can be added to show that the contribution of all the influence Variables taken together is just slight, incomplete or effectively total, respectively. The corresponding diagrams show empty, half-full and full circles, respectively.
The demonstration of at least some connection can be compared with efficacy research in medicine.
Slang: assume influences are incomplete
If not otherwise specified, Theorymaker assumes the combined influences on a Consequence only partially determine its Level. So given a Simple Theorem with no Rule and no circle, or whose Rule does not specify how completely the Consequence is determined by the Influence(s), we can assume that the influence is incomplete - neither slight nor total.
… is equivalent to this:
A !Rule:incomplete B
See also BAT