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 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 behavior of the underlying modal formalism. For example,
it becomes far simpler to formulate modal tableau and resolution in
hybrid logic, and completeness and interpolation results can be proved
of a generality that is simply not available in modal logic. That is,
hybridization --- adding nominals and related apparatus --- seems a
fairly reliable way of curing many known weaknesses in modal logic.
For more general background on hybrid logic, and many of the key
papers, see the Hybrid Logics homepage.