Of the various sigla used in classical texts, half brackets indicate a 'non-conjectural integration', i.e. an integration provided another source.
In this case, the fragmented text is
P.Oxy. 2288.
The rest of the line is 'integrated' from remaining sources (primarily Dion. Hal., but also 3 other grammatical works).
Anyway, they are signs mostly for the specialist (papyrologist, I guess). Some feel they should be done-away with in non-specialist publications (and one particularly vocal British scholar insists they should be removed from our editions altogether) since they can distract or confuse the reader.