 A major contribution in the 1990s was the introduction of the \(\mathtt{\downarrow}\) binder. An early version of the downarrow binder was introduced by Valentin Goranko in the papers Goranko (1994) and Goranko (1996). The version of the present paper was introduced in Blackburn and Seligman (1995). Since then, hybrid logic with the \(\mathtt{\downarrow}\) binder has been extensively studied, see for example the paper Areces, Blackburn, and Marx (2001) on model-theoretic aspects of this logic. A comprehensive study of the model-theory of hybrid logic is the PhD thesis of ten Cate (2004). The paper Areces, Fervari, Hoffmann, and Martel (2018) considers the relationship between strong hybrid logics with the \(\mathtt{\downarrow}\) binder and what are called relation-changing modal logics.