  Extensionality is a well known and generally cherished feature of  classical propositional and predicate logic. Modal logic, by  contrast, is intensional. To illustrate: the substitutivity principle for sentences tells us that sentences with the same truth value can  be substituted for one another salva veritate. So suppose that John's only pets are two dogs, Algol and BASIC, say, and consider two simple sentences and their formalizations (the predicates in question indicating the obvious English counterparts): 