Propositions

Predicates

Sets

Relations

Principia Mathematica

Note: the "dots" are there to avoid parentheses. Remember Whitehead's comment on notation. The disappearance of this notation from mathematics is a harsh evaluation of Whitehead/Russell as notaters.

Lukasiewicz

+++ab*bcc means ((a+b)+(b*c))+c

Note: the point was to avoid parentheses.

Jan Lukasiewicz, Selected Works, North-Holland 1970

"Comments on Nicod's Axiom and on 'Generalized Deduction'", published in 1931 in (Polish name), Lwow. Therein is a footnote

"I came upon the idea of a parenthesis-free notation in 1924. I used that notation for the first time in my article 'On the significance and requirements of mathematical logic', Nauska Polska, Vol X, Warsaw 1929, page 610, footnote...."