  The idea of possible worlds raised the prospect of extensional  respectability for modal logic, not by rendering modal logic itself  extensional, but by endowing it with an extensional semantic theory  — one whose own logical foundation is that of classical  predicate logic and, hence, one on which possibility and necessity  can ultimately be understood along classical Tarskian lines.  Specifically, in possible world semantics, the modal operators are interpreted as quantifiers over possible worlds, as  expressed informally in the following two general principles: 