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).