Summary: Notations used by TPS and ETPS
[ A] means "A is not true".
[A B] means "A and B".
[A B] means "A or B".
[A B] means "A implies B".
[A B] means "A if and only if B".
[x A] means "For every x, A is true".
[x A] means "There exists an x such that A is true".
Bracket and Parenthesis Conventions
Outermost brackets and parentheses may be omitted.
Use the convention of association to the left. Thus,
A B C stands for [[A B] C].
A B C D stands for [[[A B] C] D].
A dot stands for a left bracket, whose mate is as far to the
right as is possible without altering the pairing of left and right
brackets already present.
A .B C stands for [A [B C]].
[A .B C] D stands for [[A [B C]] D].
When the relative scopes of several connectives of different kinds