Abstract
The aim of this dissertation is to identify the construction of models that preserve (in both directions) the truth of hybrid formulas and therefore serve to characterize the expressivity of many-valued hybrid logic based on the framework of Hansen, Bolander and Brauner. We show that generated submodels and bounded morphisms preserve the truth of hybrid formulas in both directions. We also show that bisimilarity implies hybrid equivalence in general, however, the converse is not true in general. The converse is true for a weaker notion of a bisimulation for a special set of models, the image-finite models. The second significant contribution of this project is to develop the correspondence theory for many-valued hybrid logic. We show that the algorithm ALBA(first developed by Conradie and Palmigiano) can be extended to the many-valued hybrid setting. We call this extension MV-Hybrid ALBA. As a result, we successfully identify a syntactically defined class of hybrid formulas for a many-valued hybrid language, namely inductive formulas, whose members always have a local first-order frame correspondents. This inductive class generalizes the Sahlqvist class. An appropriate duality is obtained between frames in the chosen many-valued hybrid framework and a class of algebras having certain properties in order to extend ALBA to the many-valued hybrid setting.
M.Sc. (Applied Mathematics)