Chapter 9 - Syntax and Semantics II

Question 1

An occurrence of a variable κ in a formula is _______ just in case that occurrence is in the scope of a quantifier that has κ as its variable of quantification

Answer 1

bound

Question 2

An occurrence of a variable is _______ just in cases it is not bound

Answer 2

free

Question 3

A _______ _______
φ[τ/κ] of a formula φ is the formula obtained from φ by replacing all free occurrences of κ by τ, if φ has such occurrences. If φ does not have free occurrences of κ, then φ[τ/κ] is identical to φ. For quantified formulae (∀κ)φ or (∃κ)φ, we call φ[τ/κ] a substitution instance of (∀κ)φ and (∃κ)φ, respectively.

Answer 3

substitution instance

Question 4

The conclusion of an argument of predicate logic is a ______ ______ of its premises if and only if any interpretation that makes all the premises true also makes the conclusion true.

Answer 4

logical consequence

Question 5

An argument of predicate logic is _______ if and only if its conclusion is a logical consequence of its premises.

Answer 5

valid

Question 6

An argument is _______ in case it is not valid, that is, if there is a counterexample interpretation that makes the premises true, but the conclusion false.

Answer 6

invalid