# The Syntax of the Logical Language used by the Peirce Alpha Graph Builder

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