 This way of encoding Russell’s theory preserves his central claim. While there may be a certain boy that a speaker refers to in saying ‘The boy sang’, that boy is not a constituent of the quantificational proposition expressed with ‘\(!x:\textrm{Boy}(x)[\textrm{Sang}(x)]\)’; see Neale (1990) for discussion. But far from showing that the logical form of ‘The boy sang’ diverges dramatically from its grammatical form, the restricted quantifier notation suggests that the logical form closely parallels the grammatical form. For ‘the boy’ and ‘the’ do correspond to constituents of ‘\(!x:B(x)[S(x)]\)’, at least if we allow for logical forms that represent quantificational propositions in terms of second-order relations; see Montague (1970), and for discussion of relevant constraints on how such relations can be expressed with quantificational determiners, see Barwise and Cooper (1981), Higginbotham and May (1981), Keenan (1996), and the article on  generalized quantifiers.