I'm reading a pretty old paper. The authors deem "the most appropriate symbolism [...] that of Language II of Carnap, augmented with various notations drawn from Russell and Whitehead, incuding the Principia convention for dots." A few sentences later, they say
[...] we shall intrudce a functor $S$, whose value for a porperty $P$ is the property which holds of a number when $P$ holds of its predecessor; it is defined by $S(P)(t).\equiv.P(Kx).t =x')$.
This notation is new to me and I have no idea what it means. I do not understand the dots in $.\equiv.$ nor why is there a final parenthesis $)$ which has no matching left parenthesis $($. Also I do not understand the dot notation in $P(Kx).t$ nor what $x'$ stands for. Of course, this follows from the fact that I do not know anything of Carnap's Language II nor what was the language of Russell's and Whitehead Principia.
I googled "Carnap's Language II" and similar querys but I found nothing which teaches this symbolism. Could anyone $a.$ explain the meaning of these symbols and/or $b.$ point to a reference where I could learn the language in question?
Thanks in advance.