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:
Pis a proposition by this rule.
Rare propositions by the above rule, all of their concatenations are propositions, too, e.g.
PQRis a proposition by the above rules, so are
((PQR)), and so on, by this rule.
© Christian Gottschall / firstname.lastname@example.org / 2012-03-31 01:19:53