Model theory for extended modal languages Balder David ten Cate Abstract: Model theory for extended modal languages Balder David ten Cate In this thesis, several extensions of the basic modal language are studied. Model theoretic and computational properties of these extensions are investigated. Roughly speaking, the thesis contains two types of results. The first type of results can be seen as addressing specific cells in a big table along the following two dimensions. > Extensions of the basic modal language The basic modal language, the hybrid languages H, H(@) and H(E), the bounded fragment and H(@,!), guarded fragments, relation algebra and second order propositional modal logic > Model theoretic and computational properties Expressivity, frame definability, axiomatization, interpolation, the Beth property and complexity The second type of results establish cross-connections between languages. In particular, a number of truth- or satisfiability- preserving translations between different languages are described, and certain languages are characterized in terms of others (for instance, as being a model theoretically interesting fragment, or as being the smallest extension satisfying certain properties).