Editing Polish notation (section)

==Polish notation for logic==
The table below shows the core of [[Jan Łukasiewicz]]'s notation in modern logic. Some letters in the Polish notation table stand for particular words in [[Polish language|Polish]], as shown:

{| class=wikitable
|-
!Concept!!Conventional<br/> notation!!Polish<br/> notation!!Polish<br/>term
|-
|- style="border-top:3px solid #999;"
|-
|[[Negation]]||<math>\neg\phi</math>||<math> N\phi</math><ref name="Łukasiewicz_1929"/>{{rp|pages=27–28}}||{{lang|pl|negacja}}
|-
|[[Material conditional]]||<math>\phi\to\psi</math>||<math>C\phi\psi</math><ref name="Łukasiewicz_1929"/>{{rp|pages=28–31}}||{{lang|pl|implikacja}}
|-
|[[Disjunction]]||<math>\phi\lor\psi</math>||<math>A\phi\psi</math><ref name="Łukasiewicz_1929"/>{{rp|pages=34–35}}||{{lang|pl|alternatywa}}
|-
|[[Logical conjunction|Conjunction]]||<math>\phi\land\psi</math>||<math>K\phi\psi</math><ref name="Łukasiewicz_1929"/>{{rp|pages=35–36}}||{{lang|pl|koniunkcja}}
|-
|[[Sheffer stroke|Non-conjunction]]||<math>\phi\mid\psi </math>||<math>D\phi\psi</math><ref name="Łukasiewicz_1929"/>{{rp|page=36}}||{{lang|pl|dysjunkcja}}
|-
|[[Biconditional]]||<math>\phi\leftrightarrow\psi</math>||<math>E\phi\psi</math><ref name="Łukasiewicz_1929"/>{{rp|page=37}} or <math>Q\phi\psi</math><ref name="Łukasiewicz_1957"/>{{rp|page=108}}||{{lang|pl|ekwiwalencja}}
|-
|[[Universal quantification|Universal quantifier]]||<math>\forall p\,\phi</math>||<math>\varPi p\,\phi</math><ref name="Łukasiewicz_1929"/>{{rp|pages=154–156}}||{{lang|pl|kwantyfikator ogólny}}
|-
|[[Existential quantification|Existential quantifier]]||<math>\exists p\,\phi</math>||<math>\varSigma p\,\phi</math><ref name="Łukasiewicz_1929"/>{{rp|page=157}}||{{lang|pl|kwantyfikator szczegółowy}}
|-
|[[Verum]]||<math>\top</math>||<math>V</math><ref name="Łukasiewicz_1939"/>{{rp|page=275}}||{{lang|pl|prawda, prawdziwy}}
|-
|[[Falsum]]||<math>\bot</math>||<math>O</math><ref name="Łukasiewicz_1939"/>{{rp|page=275}}||{{lang|pl|fałsz, fałszywy}}
|-
|[[Modal logic|Possibility]]||<math>\Diamond\phi</math>||<math>M\phi</math><ref name="Łukasiewicz_1930x"/>{{rp|page=52}}<ref name="Łukasiewicz_1957"/>{{rp|page=134}} or <math>\varDelta\phi</math><ref name="Łukasiewicz_1953"/>{{rp|page=111}}||{{lang|pl|możliwość}}
|-
|[[Modal logic|Necessity]]||<math>\Box\phi</math>||<math>L\phi</math><ref name="Łukasiewicz_1957"/>{{rp|page=134}} or <math>\varGamma\phi</math><ref name="Łukasiewicz_1953"/>{{rp|page=111}}||{{lang|pl|konieczność}}
|}

The [[quantifier (logic)|quantifiers]] ranged over propositional values in Łukasiewicz's work on many-valued logics.

[[Józef Maria Bocheński|Bocheński]] introduced a system of Polish notation that names all 16 binary [[logical connective|connectives]] of classical [[propositional logic]].<ref name="Bochenski_1949"/>{{rp|page=16}} For classical propositional logic, it is a compatible extension of the notation of Łukasiewicz. But the notations are incompatible in the sense that Bocheński uses <math>L</math> and <math>M</math> (for nonimplication and converse nonimplication) in propositional logic and Łukasiewicz uses <math>L</math> and <math>M</math> in modal logic.