Remarks on Hybrid Modal Logic with Propositional Quantfiers

Arthur Prior invented hybrid logic, and sometimes defined nominals withhis푄operator, which he in turn defined using propositional quantifiers.Nowadays there are two well-known approaches to propositional quan-tification: the standard (or set-theoretical) approach and the general(or Henkin) approach. As we shall see, these give rise to two different‘species’ of nominals. Working in a version of hybrid logic which con-tainsbothstandard nominals and propositional quantifiers we shall seethat these two ‘species’ behave differently with respect to the rule of uni-versal instantiation. We then suggest that this formally-defined ‘speciesdivision’ corresponds rather well with two intuitions about nominals thatcan be detected in Prior’s writing: the ‘index’ view and the ‘content’ view.