7
First Order Logic = FO
t      ::= c | x
f ::= R(t, …, t) | t=t | f Æ f |  f Ç f | : f |  9 x. f | 8 x.f
Vocabulary: s = {R1, …, Rn, c1, …, cm}
Variables: x1, x2, …
In the future:
Second Order Logic = SO
Add:
f ::= 9 R. f | 8 R.f
This is SYNTAX