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

S: = S ∪ {variable or constant / term};
Q: = P[variable or constant / term];
End;
End Case of;
End while;
If P or Q contain a Next-symbol Then Unify: = fail
Else Unify: = Success;
End.
5.10 Robinson’s Inference Rule
Consider predicates P, Q1, Q2 and R. Let us assume that with appropriate
substitution S, Q1 [S] = Q2 [S] .
Then (P ∨ Q1) ∧ (Q2 ∨ R) with Q1 [S] = Q2 [S] yields ( P ∨ R) [S].
P ∨ Q1, ¬Q 2 ∨ R Q 1 [S] = Q 2 [S]
Symbolically, ______________________________
(P ∨ R) [S]
The above rule is referred to as Robinson’s inference rule [8]. It is also
referred to as the resolution principle in predicate logic. The following
example illustrates the rule.
Let P = Loves (X, father-of (X)),
Q1= Likes (X, mother-of (X))),
Q2 = Likes( john, Y),
R = Hates (X, Y).
After unifying Q1 and Q2, we have
Q= Q1 = Q2 =Likes (john, mother-of (john))
Where the substitution S is given by
S= { john /X, mother-of (X) / Y}
= {john / X, mother-of (john) / Y}.
The resolvent (P ∨ R) [s] is, thus, computed as follows.
( P ∨ R) [S]
=Loves (john, father-of (john)) ∨ hates (john, mother-of(john)).