Hybrid logic is a branch of modal logic in which it is possible to directly refer to worlds/times/states or whatever the elements of the (Kripke) model are meant to represent. Although they date back to Arthur Prior’s work in the late 1960s, and have been sporadically investigated ever since, it is only in the 1990s that work on them really got into its stride.

It is easy to justify interest in hybrid logic on applied grounds, with the usefulness of the additional expressive power. For example, when reasoning about time one often wants to build up a series of assertions about what happens at a particular instant, and standard modal formalisms do not allow this. What is less obvious is that the route hybrid logic takes to overcome this problem (the basic mechanism being to add nominals --- atomic symbols true at a unique point --- together with extra modalities to exploit them) often actually improves the behaviour of the underlying modal formalism. For example, it becomes far simpler to formulate modal tableau systems, resolution, and natural deduction in hybrid logic, and completeness results can be proved of a generality that is simply not available in ordinary modal logic. That is, hybridization --- adding nominals and related apparatus --- seems a reliable way of curing many known weaknesses in ordinary modal logic.