 A number of papers have dealt with axioms for hybrid logic, for example Gargov and Goranko (1993), Blackburn (1993), and Blackburn and Tzakova (1999). In the paper Gargov and Goranko (1993) an axiom system for hybrid logic is given, and it is shown that if the system is extended with a set of additional axioms which are pure formulas (that is, formulas where all propositional symbols are nominals), then the extended axiom system is complete with respect to the class of frames validating the axioms in question. Pure formulas correspond to first-order conditions on the accessibility relation (cf. the translation \(\mathrm{ST}_\mathtt{a}\) above), so axiom systems for new hybrid logics with first-order conditions on the accessibility relation can be obtained in a uniform way simply by adding axioms as appropriate. So, if, for example, the formula \(\mathtt{c\rightarrow \Box \neg c}\) is added as an axiom, then the resulting system is complete with respect to irreflexive frames, as we mentioned earlier. See the discussion of such rules in Section 4 of the paper Blackburn (2000).