On pg. 31 of Girle's Modal Logics and Philosophy he starts describing various modal logics in set theoretic notation, where the sets denoted are referencing truth-tree formation rules in the context of the semantic tableaux method he uses in the text.
For example to describe S4 he (apparently following Hintikka) writes the following:
$HS4Tr = SW \cup \{\Diamond R,\Box R, \Box T, \Box\Box R\}$
So, I understand the set-theoretic backdrop of the possible worlds semantics for modal logics. But this seems to be a set-theoretic backdrop for tree-formation rules, i.e. a syntactic topic. So what exactly are these sets sets of? Possible worlds too somehow? Well formed strings of symbols whose graphic construction sequences the rules represent?
Thanks so much for any insight!