Sorry for the very belated reply, but I was struggling to find the words to describe exactly what I meant. Luckily, Eliezer has already done most of it for me in his latest post.

Thing A exists with respect to Thing B iff Thing A and Thing B are both part of the same causal network. So ArisKatsaris was half-right, but things outside our past and future light cones can be said to exist with respect to us if they have a causal relationship with anything that is inside our past and future light cones.