Page 144 - Intelligent Communication Systems
P. 144
CHAPTER 10 / BASIC TECHNOLOGY OF THE INTELLIGENT COMMUNICATION SYSTEM I 23
FIGURE 10.13 Resolution example 1.
(P b P 2,. • -,/*«) -> Q = T -> T = Tis proven and is valid. If (P lt P 2,..., P B) is false,
(P,, P 2,...,Pn)-*Q is true, no matter what the value of Q is. Therefore, if and only
if (Pj, P 2,..., P n) —» j2 is vah'd, then <2 is a logical consequence of (P ls P 2,..., P w).
Example: To prove that <2 is a logical consequence of (P t A P 2 A--A P n), it must
be proved that (Pj A P 2 A A A P n) -> Q is true. Instead of proving this expression, it
is enough to prove that ~{(P] A P 2 A-A P n) —> £)} is false. ~{(Pi A P 2 A-A P n) —> Q}
A ~Q) is proved to be
is transformed to (P } A P 2 A-A P n A ~Q). If (P] A P 2 A-A P n
false, then (P,, A P 2 A-A P n) —> (2 is true.
10.4.7 Horn Set
A clause set C is a conjunction of Q, C 2,..., C n. A clause is a disjunction of liter-
als, where a literal is an atomic formula or a negation of an atomic formula. Then
a clause C is represented as follows:
Equation (8) is transformed as follows:
Considering the right side of Equation (9), which consists of only one atomic for-
mula, Equation (9) is shown as
Equation (10) is represented as follows:
