 The fact that hybridizing ordinary modal logic actually does give more expressive power can, for example, be seen by considering the formula \(\mathtt{{\downarrow} c\Box \neg c}\). It is straightforward to check that this formula is valid in a frame if and only if the frame is irreflexive. Thus, irreflexivity can be expressed by a hybrid-logical formula, but it is well known that it cannot be expressed by any formula of ordinary modal logic. Irreflexivity can actually be expressed just by adding nominals to ordinary modal logic, namely by the formula \(\mathtt{c\rightarrow \Box \neg c}\). Other examples of properties expressible in hybrid logic, but not in ordinary modal logic, are asymmetry (expressed by \(\mathtt{c \rightarrow \Box \neg \Diamond c }\)), antisymmetry (expressed by \(\mathtt{c\rightarrow \Box(\Diamond c \rightarrow c)}\)), and universality (expressed by \(\mathtt{\Diamond c}\)).