Elementary Logic

Bound Variables Formally Defined
For a formula A, the set BV (A) of bound variables in A is defined
inductively as follows:
BV (P(t 1 , t 2 , · · · , t n )) = ∅, for an n-ary predicate P applied to n
terms t 1 , t 2 , · · · , t n ;
BV (t 1 = t 2 ) = ∅;
BV (¬B) = BV (B);
BV (B ∗ C) = BV (B) ∪ BV (C), where ∗ ∈ {∧, ∨, →, ↔};
BV (⊥) = ∅;
BV (∀xB) = BV (B) ∪ {x};
BV (∃xB) = BV (B) ∪ {x}.
Yih-Kuen Tsay (SVVRL @ IM.NTU) Elementary Logic FLOLAC 2011 45 / 64