Editing Propositional calculus (section)

=== Notation styles ===
Different authors vary to some extent regarding which inference rules they give, which will be noted. More striking to the look and feel of a proof, however, is the variation in notation styles. The {{section link||Gentzen notation}}, which was covered earlier for a short argument, can actually be stacked to produce large tree-shaped natural deduction proofs<ref name=":40" /><ref name=":3" />—not to be confused with "truth trees", which is another name for [[Method of analytic tableaux|analytic tableaux]].<ref name=":37" /> There is also a style due to [[Stanisław Jaśkowski]], where the formulas in the proof are written inside various nested boxes,<ref name=":40" /> and there is a simplification of Jaśkowski's style due to [[Frederic Fitch|Fredric Fitch]] ([[Fitch notation]]), where the boxes are simplified to simple horizontal lines beneath the introductions of suppositions, and vertical lines to the left of the lines that are under the supposition.<ref name=":40" /> Lastly, there is the only notation style which will actually be used in this article, which is due to [[Patrick Suppes]],<ref name=":40" /> but was much popularized by [[John Lemmon|E.J. Lemmon]] and [[Benson Mates]].<ref name="ms51"/> This method has the advantage that, graphically, it is the least intensive to produce and display, which made it a natural choice for the [[Wikipedia community|editor]] who wrote this part of the article, who did not understand the complex [[LaTeX]] commands that would be required to produce proofs in the other methods.

A '''proof''', then, laid out in accordance with the [[Suppes–Lemmon notation]] style,<ref name=":40" /> is a sequence of lines containing sentences,<ref name=":35" /> where each sentence is either an assumption, or the result of applying a rule of proof to earlier sentences in the sequence.<ref name=":35" /> Each '''line of proof''' is made up of a '''sentence of proof''', together with its '''annotation''', its '''assumption set''', and the current '''line number'''.<ref name=":35" /> The assumption set lists the assumptions on which the given sentence of proof depends, which are referenced by the line numbers.<ref name=":35" /> The annotation specifies which rule of proof was applied, and to which earlier lines, to yield the current sentence.<ref name=":35" /> See the {{section link||Natural deduction proof example}}.