  Spelling out this understanding in terms of worlds and the preceding  analysis of intensions, we can say that an individual a has a  property F essentially if a has F in every world in which it exists, that is, if, for all worlds w in which  a exists, a ∈ F(w). Likewise,  a has F accidentally if a has F in the  actual world @ but lacks it in some other world, that is, if a ∈ F(@) but, for some world w in which a  exists, a ∉ F(w). Thus, let  ‘G’ and ‘T’ symbolize ‘is a dog’ and ‘is someone's pet’, respectively; then,  where ‘E!x’ is short for  ‘∃y(x=y)’ (and, hence,  expresses that x exists), we have: 