Is my understanding of confidence (precision) correct?

I'm attempting to develop a genetic algorithm capable of discovering classification rules for a given data set, a number of papers make use of the confidence (precision) and coverage of a rule to define its fitness. In particular, I've been following this paper.

However, I'm not sure my understanding of the equations is correct.

In that paper, the confidence is defined as

$$\text{conf} = \frac{|P \land D|}{|P|}$$

They describe it as follows

In classification problems, confidence measure is defined as the ratio of the number of examples in P that are correctly classified as decision class of D and the number of examples in P.

Is this saying the total number of occurrences of the attributes in a given rule $$P$$ which occur in rules which have been classified as class $$D$$, by the number of attributes in $$P$$?

Where an example of a rule containing two attributes would be as follows:

(martial_status = married & age > 30)

It seems a number of papers define it differently which has led to my confusion, if anyone is able to confirm my understanding or provide an some insight that'd be great.

 P     : Refers to the set of samples in your dataset. (Selected elements)