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CHAPTER 10 / BASIC TECHNOLOGY OF THE INTELLIGENT COMMUNICATION SYSTEM I 2 1
FIGURE 10.12 Alternate semantic tree of {~P(x) v Q(a), ~Q(y) v R(y), P(f(x)), ~R(z)}.
Let's find another clausal form. In Example 4, if it is assumed that x=y - z = a,
then the semantic network in Figure 10.12 is obtained. A set of clause sets with
ground instances is defined as C" and notated as follows:
Thus, there is more than one clausal form with ground instances that are unsatis-
factory. To prove that C is unsatisfactory, do the following:
(1) Make sets of clauses with ground instances C C', ....
(2) Prove one of the sets is unsatisfactory,
10.4.4 Proof of Tautology
To prove a tautology of a clausal form
a contradiction of the clausal form is proved by making a negation of either C t,
C 2,,.. or C m. If it is proved, the clausal form is a tautology. For example, by negat-
ing C,, the clausal form is described as follows:
If clausal form (2) is a contradiction, then clausal form (1) is a tautology.
There is a universal quantifier V and an existential quantifier 3 in logical
expressions. Consider the following example:
