Adding Intensional Machinery to Hybrid Logic

In this article we give an intensional version of first-order hybrid logic (which also can be viewed as a hybridized version of Fitting's First-Order Intensional Logic). We consider two different kinds of models—standard models and generalized models. The standard models are the same as Fitting's models for First-Order Intensional Logic. As the name suggests, the generalized models are more general. We give a natural deduction system which is completete with respect to generalized models. The natural deduction system is not complete with respect to standard models, but we show how to extend it with a further rule such that completeness with respect to standard models is obtained.