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

C2 = (C-(C1-{L1})θ1) θ2 -1 ∪ L2. (13.16)
Further, L2 = ¬ L1θ1θ2 -1 . (13.17)
Substituting (13.17) in (13.16) we find
C2 = (C-(C1-{L1})θ1)θ2 -1 ∪ (¬L1θ1θ2 -1 ) (13.18)
The last expression describes an inverse resolution process. It is to be
noted that θ2 -1 stands for inverse substitution, i.e. replacing constants by terms.
As an example, consider the two step inverse resolution shown in fig.
13.14, which ultimately yields a new piece of knowledge:
Grandfather (X, Z) ← Mother (Y, Z) ∧ Father (X, Y).
Let us now verify the steps of the computation .
First C1 = Father (janak, sita) =L1 and
C = Grandfather ( janak, lob).
Here, θ1={ } and θ2 -1 ={ X / janak }.
So, [C- (C1-{L1}) θ1] θ2 -1
= (Cθ1) θ2 -1
= Grandfather (X, lob)
Further, ¬L1θ1 θ2 -1 = ¬Father (X, sita).
Thus the derived clause by (13.18) is Grandfather (X, lob) ∨ ¬Father(X, sita).
The second step of inverse resolution can be verified easily in a similar
manner.
13.6 Computational Learning Theory
The main question on machine learning is: how does one know that his
learning algorithm has generated a concept, appropriate for predicting the
future correctly? For instance, in inductive learning how can we assert that our
hypothesis h is sufficiently close to the target function f, when we do not