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 wff is “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).