The theory of constructive types (principles of logic and mathematics). By Leon Chwistek.

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definitions given by this author (to be given below) we shall.
have':..*pI.- p V \/q..
0'11 Any expression denoting logical proposition is a propositional expression..
0 12 Propositional (or f u a c t i on a 1) expressions are s i g n i fi e a n t.
they have a mea nni n in isolation.
0'13 If 2 is any primitive or fundamental variable ur any functional expression and 5 'î, ~, ~ ' any individual or fundamental
variables or any funietional expressions: then the expressions
2t}, {,0 'j, 2{, i ~'}7t {,,,, } are f un c t io n al pa tterns with 7 - with I with IIf, or with IV argum e n t s. flere  is a fu n c t i o si a 1; i g ni,,, # are arguments belonging to a,
0~131 In functional.patterns 2{Â}:. t{ '} or 2{,1}, b { ', /}, or
2 {' 7, '}, H {$, <,i 'X 2 or 2 0{, 12! ~:;}, >t `^, 9, '&' 5' the
arguments 3, 3' where 8 is c or l, or q or ~. are corresponding arguments.
0'1311. Any functional pattern, whose functional sign is a primitive
or fundamental al revariable and whose arguments are individual real variables, is a propositional expression
01232 If in a significant expression E, the fitndamnental variable
and a functional expression M1 having no letters in common
with l are corresponding arguments belonging to the sarie
functional sign: then e is a determined variable, or a
variable determined b y M.
0 14 If El(), or -E(2, q), or 1H(,, i v), or i(2, ), a r) are any
propositi l pressions continuing the individual, primitive,
or determined real veriables: ', or:, o, or 2,, v, or \, v,,:
thent hee expressions: [EL()], or ( [G(4, ( )1, or,iv[H(, y, v):,
or fiv[I, Qr v, ~)] are functional expressions with I, or
with Il, or with 1 1, or with IV variables. Here we have turned real. variables into note d variables.
04141 If E('): (,, HG(), ( ), (t, V), I( 'v) Q are any expressions
containing the noted variables,: or 2 it,) or 2),q v, or
2,9;, r, v and if [E(S)],2;^iC[G(, )i \iÂ' [((',\ r )^],
2 () [1(2, il 1 Q)-1 are fulletio-ial expressions, then the expres