Page 141 - Intelligent Communication Systems

I 20 INTELLIGENT COMMUNICATION SYSTEMS

FIGURE 10.10 Semantic tree of (~P(a) v Q(b), ~Q(x) v R(y), P( Z), ~R(w)}.

FIGURE 10.11 Semantic tree of {-/>(*) v Q(a), ~Q(y) v R(y\ P(f(x)\ ~R(z)}.

Example 5: The following clause set is given:
C = {-/>(*) v Q(a\ ~Q(y) v R(y\ P(f(x)), ~R(z)}
The Herbrand universe and Herbrand base are as follows:

H(C)= (a,/(a),/(/(a)),/(/(a)), ...},
HB(Q = {P(a\ Q(a\ R(a\ P(/(a)), Q(f(a)\ R(f(a)), ...}

A semantic tree is shown in Figure 10.11. Because the tree has failure nodes on all
of the branches, a clause set C is unsatisfactory. A set of clauses with ground
instances is defined as C* and notated as follows:
C = (~P(a) v Q(a), ~P(f(a)) v Q(a\ ~Q(a) v R(a), P(f(a)\ ~R(d)}