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

13.5 Learning by Inductive Logic
Programming
Inductive logic programming (ILP) employs an inductive method on the first
order clauses through a process of inverse resolution. The ILP can generate
new predicates and is therefore called constructive induction.
Let us first start with the resolution theorem of predicate logic.
Suppose we have two clauses C1 and C2 given by
C1 = Male(X) ← Boy(X)
and C2 = Boy(ram).
So, C1 = ¬ Boy(X) ∨ Male(X). (13.10)
Let literal L1 = ¬ Boy (X) (13.11)
and L2 = Boy (ram) (13.12)
Let the unifying substitution θ={ram / X}. We can now write
L1θ = ¬ L2θ = ¬ Boy (ram). Now, after resolving C1 and C2, suppose we obtain
the resolvent C, where
C = Male(ram). Thus C is the union of (C1-{L1})θ = Male(Ram)
and (C2-{L2})θ = φ.
Formally, we can always write C = (C1-{L1})θ ∪ (C2-{L2})θ (13.13)
The unifying substitution θ can be factored to θ1 and θ2 [10], i.e.
θ = θ1θ2 (13.14)
where θ1 contains all the substitutions involving variables from clause C1 and
θ2 contains all the substitutions involving variables from C2. Thus
C = (C1-{L1})θ1 ∪ (C2-{L2})θ2
where '–' denotes set difference operator. We can re-express the above as
C – (C1-{L1})θ1 = (C2-{L2})θ2 (13.15)
which finally yields