# What is the origin of the prefix logic notation used in WFF 'N PROOF?

The classic "modern logic" game of WFF 'N PROOF uses a set of symbols to represent logical relations that I've seen used nowhere else: $C$ for then; $A$ for or; $K$ for and; $E$ for if and only if; and $N$ for not. These are used in prefix notation so that, for example $$CNpq$$ means $$\neg p\Rightarrow q,$$ and $$EpAqNr$$ means $$p\Leftrightarrow \left({q\vee\neg r}\right).$$

What is the origin of these symbols and have they been used widely or elsewhere? Are they still in use?

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Your link contains a recent forum thread debating that very question. – Henning Makholm Oct 4 '11 at 18:52

It's polish notation. For example, $K$ stands for koniunkcja, from the same root as "conjunction".

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It was called "Polish notation" because of people who could not remember the name Łukasiewicz. – GEdgar Oct 4 '11 at 18:47
Some examples of the use of this notation. – raxacoricofallapatorius Oct 5 '11 at 12:48

The "Polish" notation was introduced by my academic grandfather, Jan Łukasiewicz (1878-1956).

A famous joint paper with Tarski, "Untersuchungen über den Aussagenkalkül," (1930) contains the phrase "Łukasiewicz employs the formulas Cpq and Np." A footnote indicates that Łukasiewicz used the notation in a paper from 1929 and in his famous text Elementy logiki matematycznej (1929) which contains the contents of a course given "in the autumn trimester of the academic year 1928/9". In a paper by Łukasiewicz from 1931 a footnote reports that "I came upon the idea of a parenthesis-free notation in 1924." Thus 1924 seems to be the most likely date of the creation of Łukasiewicz's parenthese free notation.

The notation has been, and continues to be, widely used in the study of propositional calculi.

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This answer deserves to get accepted. By "academic grandfather" do you mean that your thesis adviser had Łukasiewicz as his/her thesis adviser (or someone further down the line)? Also, and I guess this wanders a bit... I've read that C. A. Meredith developed condensed detachment building on Łukasiewicz's work. I'd like to know how he did this, but I don't have access to his work. Did Meredith basically get the idea or build on the way in Łukasiewicz notated his proofs? – Doug Spoonwood Jun 15 '13 at 2:55
On the work of C. A. Meredith, see "In memoriam: Carew Arthur Meredith (1904--1976)" Notre Dame Journal of Formal Logic, Volume 18, Number 4 (1977), 513-516, by his cousin David Meredith. Google – Fred Rickey Jun 15 '13 at 3:52
The paper is on line: projecteuclid.org/euclid.ndjfl/1093888116. Yes, my advisor, Boleslaw Sobocinski was a PhD student of Łukasiewicz. – Fred Rickey Jun 15 '13 at 4:03