1.1.9 Notation

Introduction of some abbreviations for first-order syntax.

In what follows, we won't always be adhering to the official first-order syntax defined above. Instead, we'll generally try and use as few brackets as possible, as this tends to improve readability. For example, we would rather not write

Outer Brackets.

which is the official syntax. Instead, we are (almost invariably) going to drop the outermost brackets and write

Precedence.

To help further reduce the bracket count, we assume the following precedence conventions for the Boolean connectives: takes precedence over and , both of which take precedence over . What this means, for example, is that the formula

is shorthand for the following:

In addition, we'll at the same time use the square brackets ] and [ as well as the official round brackets, as this can make the intended grouping of symbols easier to grasp visually.