Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

know f ? These questions can be answered with the help of computational
learning theory.
Mother (sita, lob)
The principle of computational learning theory states that any
hypothesis, which is sufficiently incorrect, will be detected with a high
probability after experimenting with a small number of training instances.
Consequently, a hypothesis that is supported by a large number of problem
instances will be unlikely to be wrong and hence should be Probably
Approximately Correct (PAC).
The PAC learning was defined in the last paragraph w.r.t. training
instances. But what about the validity of PAC learning on the test set (not the
training set) of data. The assumption made here is that the training and the test
data are selected randomly from the population space with the same
probability distribution. This in PAC learning theory is referred to as
stationary assumption.
[13].
Grandfather (X, Z) ∨ ¬ Mother (Y, Z ) ∨ ¬ Father (X, Y)
Grandfather ( X, lob) V ¬ Father (X, sita)
Father (janak, sita)
Grandfather (janak , lob )
In order to formalize the PAC learning theory, we need a few notations
Let X = exhaustive set of examples,
{Y / sita , Z / lob}
{ X / janak }
Fig. 13.14: A two step inverse resolution to derive: Mother (Y, Z) ∧
Father (X, Y) →Grandfather (X,Z).