In his book Aboutness, Stephen Yablo gives a definition of 'being true about'. A sentence can be false, but sill be true about part of its subject matter, and Yablo tries to capture this using a possible worlds analysis.
I wrote a small post about why I think his construction fails: https://lilith.cc/~victor/dagboek/index.php/2026/05/11/yablo-on-being-true-about/