Editing Natural deduction (section)

===History of notation styles===
Natural deduction has had a large variety of notation styles,{{sfn|Pelletier|Hazen|2024}} which can make it difficult to recognize a proof if you're not familiar with one of them. To help with this situation, this article has a {{section link||Notation}} section explaining how to read all the notation that it will actually use. This section just explains the historical evolution of notation styles, most of which cannot be shown because there are no illustrations available under a [[public copyright license]] – the reader is pointed to the [https://plato.stanford.edu/archives/spr2024/entries/natural-deduction/ SEP] and [https://iep.utm.edu/natural-deduction/ IEP] for pictures.
* [[Gerhard Gentzen|Gentzen]] invented natural deduction using tree-shaped proofs – see {{section link||Gentzen's tree notation}} for details.
* [[Stanisław Jaśkowski|Jaśkowski]] changed this to a notation that used various nested boxes.{{sfn|Pelletier|Hazen|2024}}
* [[Frederic Fitch|Fitch]] changed Jaśkowski method of drawing the boxes, creating [[Fitch notation]].{{sfn|Pelletier|Hazen|2024}}
* 1940: In a textbook, [[Willard Van Orman Quine|Quine]]<ref>{{harvtxt|Quine|1981}}. See particularly pages 91–93 for Quine's line-number notation for antecedent dependencies.</ref> indicated antecedent dependencies by line numbers in square brackets, anticipating Suppes' 1957 line-number notation.
* 1950: In a textbook, {{harvtxt|Quine|1982|pp=241–255}} demonstrated a method of using one or more asterisks to the left of each line of proof to indicate dependencies. This is equivalent to Kleene's vertical bars. (It is not totally clear if Quine's asterisk notation appeared in the original 1950 edition or was added in a later edition.)
* 1957: An introduction to practical logic theorem proving in a textbook by {{harvtxt|Suppes|1999|pp=25–150}}. This indicated dependencies (i.e. antecedent propositions) by line numbers at the left of each line.
* 1963: {{harvtxt|Stoll|1979|pp=183–190, 215–219}} uses sets of line numbers to indicate antecedent dependencies of the lines of sequential logical arguments based on natural deduction inference rules.
* 1965: The entire textbook by {{harvtxt|Lemmon|1978}} is an introduction to logic proofs using a method based on that of [[Patrick Suppes|Suppes]], what is now known as [[Suppes–Lemmon notation]].
* 1967: In a textbook, {{harvtxt|Kleene|2002|pp=50–58, 128–130}} briefly demonstrated two kinds of practical logic proofs, one system using explicit quotations of antecedent propositions on the left of each line, the other system using vertical bar-lines on the left to indicate dependencies.{{refn|A particular advantage of Kleene's tabular natural deduction systems is that he proves the validity of the inference rules for both propositional calculus and predicate calculus. See {{harvnb|Kleene|2002|pp=44–45, 118–119}}.}}