A PAC-like analogue for 1-class classification? This is more of a philosophical question -- I am looking for a reasonable mathematical formulation of 1-class learning.

In the PAC model, it's very natural to formulate our demand on the learner: produce a hypothesis with low generalization error.

What might be a reasonable formalization of 1-class learning? This may also be called "anomaly detection": in the training phase, the learner only gets to see positive ("normal") examples, but in the test phase he needs to predict whether a given new example is positive ("normal") or negative (an anomaly). The formal details are quite open-ended -- what's a reasonable assumption on the training sample (generated from some distribution, etc)? What's a reasonable success criterion?
I think there is a model called "Learning from Positive Examples (Only)" or you can additionally allow unlabeled data (I don't remember the details).  A search for these terms should bring up various papers and models.  Here is one.