Notatio Polonica

Notatio Polonica, etiam notatio praefixorum Polonica vel simpliciter notatio praefixorum, est genus notationis in usu in logica, arithmetica, et algebra. Sua proprietas unica est operatores ad sinistram eorum operandorum ponere. Si aritas operatorum certa sit, eventus est syntax parenthesibus vel aliis uncis carens qui sine ambiguitate iam describi potest. Ioannes Łukasiewicz, logicus Polonus, hanc notationem anno 1924 excogitavit ut logicam sententialem faciliorem reddat.

Alonzus Church in libro classico de logica mathematica hanc rationem commemorat, quam dignam notationis aestimat in rationibus notationis adeo contra expositionem notationis logicae Alfredi North Whitehead et Bertrandi Russell et eorum opus in libro Principiis Mathematicis.^[1]

Notatio Polonica in logica recensere

Tabula infra data nucleum notationis Ioannis Łukasiewicz pro logica sententiali excogitatae monstrat.^[2] Nonnullae litterae in tabula certa verba in lingua Polonica significant.

Sententia	Notatio usitata	Notatio Polonica	Verbum Polonicum
Negatio	$\neg \varphi$	$\mathrm {N} \varphi$	negacja
Coniunctio	$\varphi$ ∧ $\psi$	$\mathrm {K} \varphi \psi$	koniunkcja
Disiunctio	$\varphi$ ∨ $\psi$	$\mathrm {A} \varphi \psi$	alternatywa
Conditionale materiale	$\varphi \to \psi$	$\mathrm {C} \varphi \psi$	implikacja
Biconditionale	$\varphi \leftrightarrow \psi$	$\mathrm {E} \varphi \psi$	ekwiwalencja
Falsum	$\bot$	$\mathrm {O}$	fałsz
Ictus Shefferanus	$\varphi \mid \psi$	$\mathrm {D} \varphi \psi$	dysjunkcja
Possibilitas	$\Diamond \varphi$	$\mathrm {M} \varphi$	możliwość
Necessitas	$\Box \varphi$	$\mathrm {L} \varphi$	konieczność
Quantificator universalis	$\forall p\,\varphi$	$\Pi p\,\varphi$	kwantyfikator ogólny
Quantificator existentialis	$\exists p\,\varphi$	$\Sigma p\,\varphi$	kwantyfikator szczegółowy

↑ Church 1944:38: "Worthy of remark is the parenthesis-free notation of Jan Łukasiewicz. In this the letters N, A, C, E, K are used in the roles of negation, disjunction, implication, equivalence, conjunction respectively."
↑ Craig 1998:496.

Church, Alonzo.1944. Introduction to Mathematical Logic. Princetoniae: Princeton University Press.
Craig, Edward. 1998. Routledge Encyclopedia of Philosophy, 8. Taylor & Francis. ISBN 9780415073103.
Łukasiewicz, Jan. 1930, 1967. Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls. Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie 23:51–77 (1930). Conv. H. Weber ut "Philosophical Remarks on Many-Valued Systems of Propositional Logics," in Polish Logic 1920–1939, ed. Storrs McCall (Oxoniae: Clarendon Press, 1967).
Łukasiewicz, Jan 1957. Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic. Oxoniae: Oxford University Press.