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

5.9 Unification of Predicates
Two predicates P (t1,t2,..., tn) and Q (s1, s2,..., sn) can be unified if terms ti
can be replaced by si or vice-versa.
Loves (mary, Y) and Loves (X, Father-of (X)) , for instance, can be unified by
the substitution S ={ mary / X , Father-of ( mary) / Y }.
Conditions of Unification:
i) Both the predicates to be unified should have an equal number of terms.
ii) Neither ti nor si can be a negation operator, or predicate or functions of
different variables, or if ti = term belonging to si or if si = term belonging
to ti then unification is not possible.
The Unification Algorithm
Input: Predicates P(t1, t2,…, tn) and Q(s1,s2,…,sm)
Output: Decision whether the predicates P and Q are unifiable
and a set S that includes the possible substitution.
Procedure Unification (P, Q, S, unify)
Begin
S:= Null;
While P and Q contain a Next-symbol do
Begin
Symb1: = Next-symbol (P);
Symb2: = Next-symbol (Q);
If Symb1 ≠ Symb2 Then do
Begin Case of
Symb1 or Symb2 = Predicate: Unify: = fail;
Symb1 = constant and symb2 = different-constant: Unify: = fail;
Symb1 or Symb2 = ¬ : Unify: = fail;
Symb1 and Symb2 = function: Unify: = fail;
Symb1=variable and Symb2 =term and variable ∈ term: Unify: = fail;
Symb2=variable and Symb1=term and variable ∈ term: Unify: = fail;
Else If Symb1 = variable or constant and Symb2 =term Then do
Begin
S: = S ∪ {variable or constant / term};
P: = P[variable or constant / term];
End;
Else If Symb2 = variable or constant and Symb1 =term Then do
Begin