I have some measurements on a system (x, y, z, ..) over many trials. The system produces a true or false output. I would like to take my data and produce a predictor function of x,y, z, that would best predict the system outcome.
I am used to methods for approximating smooth outcomes like approximating a graph, but don't know the terms to search for when the outcome is true/false.
Search for multivariate classification.
In your case you just have two classes (true and false).
The Wikipedia article on statistical classification has a list of commonly used algorithms.
You can also search for multivariate regression which attempts to model a real value as function of several values where in your case the possible values are a discrete set (0,1).
One would have to take a decision on whether the predicted outcome is True or False based on the regression function's output (e.g. assume True if the output is > 0.5 and False if it's <= 0.5).
Note that there is also https://stats.stackexchange.com/ where you could get more detailed answers related to the analysis of data.
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