I recently read a fascinating review (in issue no. 136 of Philosophy Now) of Probably Approximately Correct written by Harvard Professor of Applied Mathematics and Computer Science, Leslie Valiant. PAC's are described as computer algorithms that allow for noisy/messy data inputs and "good enough" outputs.
They have apparently been used to quantify the extent to which a learning process with (i) no underlying theory about the problem, (ii) finite computational resources and (iii) limited access to data can make inferences and predictions; and to place bounds on the types of problem any physical system with finite/limited resources, including human brains, can perform. That is, quantify the uncertainty of the inductions/predictions one generates from experience, and diagnose how a learner can fail (task too random to be learned or too complex to permit extracting a prediction). It is claimed that the PAC's limits on time, energy, memory, etc. provide insights into the origins of cognitive biases and logical fallacies so prevalent in human thinking.
Does anyone here have any experience with the PAC algorithms and insights as to the extent to which what can be learned from them is generalizable to human brains and cognition? For instance, what is the relationship between what a PAC algorithm accomplishes and the Piercean notion of Abduction (abductive inference), characterized as the "best available" or "most likely" explanation?