  In order to keep things simple, we do not consider a full type hierarchy—first-order is enough to get the basics across. The first-order fragment of the logic of Gallin 1975 would be sufficient, for instance. The particular formulation presented here comes from Fitting 2004, extending Fitting and Mendelsohn 1998. Predicate letters are intensional, as they are in every version of Kripke-style semantics, with interpretations that depend on possible worlds. The only other intensional item considered here is that of individual concept—formally represented by constants and variables that can designate different objects in different possible worlds. The same ideas can be extended to higher types, but what the ideas contribute can already be seen at this relatively simple level. Intensional logics often have nothing but intensions—extensions are inferred but are not explicit. However, an approach that is too minimal can make life hard, so consequently here we explicitly allow both objects and individual concepts which range over objects. There are two kinds of quantification, over each of these sorts. Both extensional and intensional objects are first-class citizens.