Introduction to Soft Computing: Neuro-Fuzzy and Genetic Algorithms

 e corresponding truth table is shown in Table 3.9.  e two premises of the argument, a → (c

→ b) and a → c, are arranged in Columns 5 and 6, respectively.  e conclusion a → b is shown in

Column 7. In Rows 1, 2, 3, 4 and 8, both the premises are true.  e corresponding truth-values of

the conclusion, noted in Column 7 are also true. Hence the argument is valid

Table 3.9. Consistency checking

(1) (2) (3) (4) (5) (6) (7)

ab b

c → ba → (c → b) a → ca → b

(1) 0 0 0 1 1 1 1

(2) 0 0 1 0 1 1 1

(3) 0 1 0 1 1 1 1

(4) 0 1 1 1 1 1 1

(5) 1 0 0 1 1 0 0

(6) 1 0 1 0 0 1 0

(7) 1 1 0 1 1 0 1

(8) 1 1 1 1 1 1 1

3.1.2 Predicate Logic

 e propositional logic described above ...