Section: New Results
Logics with Concrete Domains
Another topic within the work of LED is on special reasoning methods. We study how to combine the standard satisfiability problem (for modal, description and first-order logic) with some flavour of model checking. The core idea is that we want to consider a class of models where each model has an ``abstract part'' that can vary from model to model and a ``concrete part'' that is fixed and common to all models (we can think, for example, that the concrete part is the natural numbers with some operations, or a concrete model of the discourse up to the moment in a natural language dialogue system). An example of such logics are Description Logics with Concrete Domains. Work on what was called half order modal logics also fits under this view.
The main result obtained is a general framework which evolved as an extension of previous work on hybrid logics and that provides a unified view on hybrid logics, description logics with concrete domains and half order logics  .