"Controlling" for multiple sequential association rules? Assume I have data along the following lines
A-A-B-C
A-A-B-C
A-A-B-C

Then I test the following sequential association rule: "A-A precedes C", which is true 100% of the time. However, at the same time the rule "B precedes C" is also true  100% of the time. This is obviously a silly, simplified example, but what I am trying to understand is how to "control" for other sequential association rules, in a similar way to how you would control for certain variables in a regression model.
Hence: are there any established approaches for "controlling" for multiple sequential association rules?
 A: Maybe I'm thinking to simple here, but isn't what you're looking for inherent to the apriori principle used to find the association rules in the first place?
For A-A-B-C to not be pruned, A-A-(gap)-C and B-C (and also A-A, A-B, etc.) need to be above the pruning threshold. 
A very simple heuristic would therefore be to take the "largest" pattern having the desired support (Essentially, look at the lowest level of the apriori tree). All the patterns it contains will have at least the same support by definition.
This also means that any two contained patterns are equally valid. In an intuitive example: 
If [Buys beer, buys chips, watches football] is a frequent pattern, then 
[buys chips, (gap), watches football] and 
[buys beer, watches football] will both be equally valid frequent patterns.
A: What you are considering in your example of C given A-A would actually be represented by the conditional probability 
$$
P(C | (A \cap A) \cap (A \cup B \cup C)) 
$$
This would evaluate to 100% as you said.  The conditional probability you wanted to monitor was 
$$
P(C|(A \cap A) \cap  B)
$$
and likewise you could calculate $P(C|(A \cap A) \cap  A)$ and $P(C|(A \cap A) \cap  C)$.
However, these are only a few possibly ways to fit your data.  For instance, the logic statement $P(C| (A\cap A) \cup B)$ also gives a result of 100%.  Thus, as in most machine learning problems, it all comes down to your hypothesis set and how many data points you have to work with.
Let's take for example, a hypothesis set where A, B, and C are independent events and use your three data points from above to calculate the probability $P(A) = 6/12, P(B) = 3/12$, and $P(C) = 3/12$.  To test this, we calculate the probability for 4 events which are either $A$, $B$, or $C$ from your data set.  Thus the measured probabilities are
$$
P(A,A,A,A) = 0
$$
$$
P(A,A,A,B) = 0
$$
$$
P(A,A,A,C) = 0
$$
etc... until we find $$
P(A,A,B,C) = 1;
$$
Now, if we truly had independent events our expected probability would be, 
$$
P(A,A,B,C) = (1/2)(1/2)(1/4)(1/4) = 1/64 \sim 0.016. 
$$
Now you decide if you accept or reject your hypothesis set (typically by taking the squared difference between the expected and measured values).
Keep in mind, all machine learning principles apply here so be very careful how many degrees of freedom you give your hypothesis set as you can easily over-fit this data if your not careful.  Therefore make sure to run proper validation and cross-validation checks.
More specific to your exact question, choose a hypothesis set, calculate the results, and compare those results to other possible hypothesis sets to find the best match.
