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The Syntax of awFOL

What do the brackets mean?

We define what counts as a sentence of awFOL using rules. E.g.:
1. If * and \# are sentences, then so is(* ∧ \#)
2. If * and \# are sentences, then so is (* ∨ \#)
3. P, Q, R, … are sentences
4. If * is a sentence, then ¬* is a sentence
So:
a. P is a sentence // rule 3
b. ¬P is a sentence // rule 4, a
c. ( ¬P ∧ Q ) is a sentence // rule 1, b, a
There is no structural ambiguity in awFOL because these rules are formulated to ensure that for any awFOL sentence, there is exactly one way of constructing it.