Abstract

We discussed equality at length in Chap. 11, but this was before we introduced the machinery of predicate abstraction. Recall that a model is normal if the relation symbol “=” is interpreted to be the equality relation on the domain of the model. The relation is thus the same from world to world. Now it is time to see how equality and predicate abstraction interact. While the basics of what we have to say applies to non-rigid terms generally, things are most easily understood if function symbols are not present, and that is all we discuss formally in this section. Our setting throughout this section can be assumed to be the modal logic K, with varying domains, allowing terms that may not designate, that is, K with the VN conditions. This is the most general setting we have, since all other setups are the result of putting further restrictions on this one.