Predicate logic

1. Predicate logic CSC 333

2. Terms • Universal quantifier • Existential quantifier • Predicate • Domain of Interpretation • Dummy variable • Free variable • Predicate wff • Unary, binary, ternary

3. Things to remember . . . • The order of quantifiers is important (p. 36). • Universal quantifier and implication go together. • Existential quantifier and conjunction go together.

4. English is problematic . . . • The meaning of the word “only” may depend on its placement. Even then . . . (p. 39) • The use of “not” with universal quantifier (p. 41).

5. Validity • A tautology is a propositional wff that is true for all rows of the truth table. • A predicate wff is valid if it is true in all possible interpretations; a valid wffis “intrinsically true.” • See Table 1.16

6. Inference rules using quantifiers • Universal instantiation • Consider restriction and Example 25 • Existential instantiation • Example 27 • Universal generalization • Example 28 • Existential generalization • Example 29

7. Heuristics • Predicate logic rules apply only when the exact pattern of the rule is matched. • The instantiation rules remove a quantifier from the front of the entire wff to which the quantifier applies. (P. 54) • Insertion of a quantifier must be in front of a wff that is entirely within its scope. • See “plan of attack”, p. 54.

8. Temporary hypothesis • Not often needed. • To prove P -> Q, it may be useful to assume P as a temporary hypothesis. • Can’t be used if quantifier applies to P (Example 31).