 See the handbook chapter Areces and ten Cate (2006) for a detailed account of the syntax and semantics of hybrid logic, as well as many other basic definitions. The syntax and semantics above can be extended in a number of ways, in particular, first-order quantification can be added (of course, an equivalent way to obtain first-order hybrid logic is by adding hybrid-logical machinery to first-order modal logic). See Braüner (2014) for an overview of first-order hybrid logic, see Chapter 6 of Braüner (2011a) for a more detailed account, and see Chapter 7 of Braüner (2011a) for an account of intensional first-order hybrid logic.