Modal Hybrid Logic

Axiomatizing hybrid logic using modal logic

We study hybrid logics with nominals and ‘actuality’ operators @i. We recall the method of ten Cate, Marx, and Viana to simulate hybrid logic using modalities and ‘nice’ frames, and we show that the hybrid logic of a class of frames is the modal logic of the class of its corresponding nice frames. Using these results, we show how to axiomatize the hybrid logic of any elementary class of frames....

Resolution in Modal, Description and Hybrid Logic

We provide a resolution-based proof procedure for modal, description and hybrid logic that improves on previous proposals in important ways. It avoids translations into large undecidable logics, and works directly on modal, description or hybrid logic formulas instead. In addition, by using the hybrid machinery it avoids the complexities of earlier propositional resolution-based methods for mod...

Robust Controller Synthesis for Hybrid Systems Using Modal Logic

In this paper, we formulate and robustly solve a quite general class of hybrid controller synthesis problems. The type of controller we investigate is the switching control mechanism of a hybrid automaton (via guard and mode invariant sets), and the robustness result is with respect to variations in the right hand sides of the differential equations that depend continuously on a parameter. We p...

Modal Logic

Modal Logic As Dialogical Logic

The title reflects my conviction that, viewed semantically, modal logic is fundamentally dialogical; this conviction is based on the key role played by the notion of bisimulation in modal model theory. But this dialogical conception of modal logic does not seem to apply to modal proof theory, which is notoriously messy. Nonetheless, by making use of ideas which trace back to Arthur Prior (notab...