 Note however, that some actualists may respond that they need not be committed to the actuality of possible worlds so long as it is understood that quantifiers used in their theory of language lack strong ontological import. Furthermore, Hayaki (2006) argues that quantifying over abstract entities is actually incompatible with any serious form of actualism. In any case, it is open to actualists (and non actualists as well) to investigate the logic of quantifiers with more robust domains, for example domains excluding possible worlds and other such abstract entities, and containing only the spatio-temporal particulars found in a given world. For quantifiers of this kind, a world-relative domains are appropriate.