The syntax of the Alpha part of Peirce's Existential Graphs, i.e. the
syntax of its propositional subset, is very simple. There are really
only two kinds of entities: atoms and cuts. An *atom* is a
propositional variable indicating some atomic sentence. The proof
builder allows all the letters "A" to "Z", not discerning between cases.
A *cut* is, in Peirce's work, a closed line surrounding one or
more propositions. With the proof builder, the cut is expressed using
brackets. Writing any proposition within brackets indicates that they
are enclosed by a cut. Semantically, placing some (simple or complex)
proposition within a cut means negating this proposition.

Formally, the formation rules of the language used by the Peirce Proof
Puilder (pardon, Builder) are as follows:

- Any letter is a proposition. Example:
`P`

is
a proposition by this rule.
- If any number of strings are propositions, then their
concatenation is a proposition, too. Example: Since
`P`

, `Q`

and `R`

are
propositions by the above rule, all of their concatenations
are propositions, too, e.g. `PQR`

, or
`PPPQRRQQPR`

.
- If some string is a proposition, the same string, enclosed
in brackets, is a proposition, too. Examples: Since
`PQR`

is a proposition by the above rules, so
are `(PQR)`

, `((PQR))`

, and so on, by this
rule.
- If a string is not a proposition by any of the above rules,
it is no proposition at all.

## Some example propositions

- P
- P(Q)
- P(Q(R))S(S)
- P(P(Q))

© Christian Gottschall / christian.gottschall@posteo.de / 2012-03-31 01:19:53