13 December 2011
Hybrid Logic and Henkin Models
University of Roskilde
In this talk I will motivate and introduce hybrid logic, a form of modal logic in which reference to worlds (or times, or epistemic states) is possible via special atomic symbols called nominals. The idea traces back to work by Arthur Prior, the inventor of tense logic in the 1960s, and I shall briefly discuss some of Prior's concerns, though I will concentrate on contemporary approaches.
But the main theme of the talk is to focus on the deductive effectiveness of hybrid logic, and I will do so by discussing how hybrid logic makes it possible to work with Henkin models. This is a novelty in modal logic, where canonical models are the standard technical tools for proving deductive completeness. But the approaches are quite different, and I shall attempt to convey the spirit of these differences and to make the generality of the Henkin approach clear.
I won't be assuming prior knowledge of hybrid logic, nor much knowledge of modal logic either. The hybrid approach has a certain directness and, as it is closely related to familiar ideas and techniques from first-order logic, can be readily understood and appreciated.