  Leśniewski’s own notation for Protothetic is explained in ‘Supplementary Remark III’ of the Introductory Remarks: one-place connectives are made up of a horizontal bar ‘–’ supplementable at either end by a vertical bar ‘|’. A bar at the right-hand end of the line signifies the connective gives output value T(rue) for input value T, the absence of a bar signifies the output value for input T is F(alse).  Similarly a bar at the left-hand end of the line signifies output value T for input value F, the absence of a bar signifies output F for input F. The four extensional one-place connectives are thus systematically notated, with negation, the most important, written as ‘\(\vdash\)’. For two-place connectives bars are added radially as spokes to a circular central hub ‘\(\circ\)’. As before the presence of a bar indicates an output value T, its absence an output value F. The top position is for first and second inputs F, the bottom position for first and second inputs T, the left position for first input T and second input F, the right position for first input F and second input T. Thus all sixteen possibilities are catered for. For example the conjunction connective is written ‘\(\koppa\)’. If one connective H is contained geometrically in another G, the implication G\((pq) \rightarrow\) H\((pq)\) holds, and merging two connectives gives a connective equivalent to their conjunction. While this notation is systematic and elegant, it has never caught on. Like Łukasiewicz, Leśniewski always puts the connective before its arguments, but he encloses the arguments in parentheses, thus the conjunction of \(p\) and \(q\) is written ‘\(\koppa(pq)\)’. The reason for parentheses, which Łukasiewicz could dispense with, will become clear. In this “official” notation, the only quantifier is the universal, written by placing the variables bound between lower corners, as for example ‘ \(\llcorner pqf\lrcorner\) ’, and placing the quantifier scope or matrix within upper corners, so for example ‘\(\llcorner pqf\lrcorner \ulcorner \koppa(f(pq)f(qp))\urcorner\)’ is Leśniewski’s way of writing what we write as ‘\(\forall pqf\ulcorner f(pq) \wedge f(qp)\urcorner\)’. In his everyday logical work and derivations however, Leśniewski used a slightly modified version of Whitehead and Russell’s Principia Mathematica notation.