On Extensions and Variants of Dependence Logic — A study of intuitionistic connectives in the team semantics setting

Dependence logic is a new logic which incorporates the notion of “dependence”, as well as “independence” between variables into first-order logic. In this thesis, we study extensions and variants of dependence logic on the first-order, propositional and modal level. In particular, the role of intuitionistic connectives in this setting is emphasized. We obtain, among others, the following results: • First-order dependence logic extended with intuitionistic and linear connectives characterizes all second-order downwards monotone properties. • First-order independence logic extended with intuitionistic and linear connectives, and first-order inclusion logic extended with maximal implication are both equivalent to the full second-order logic over sentences. • Complete axiomatizations for propositional dependence logic, propositional intuitionistic dependence logic, propositional independence logic extended with nonempty atom. • Intuitionistic connectives are definable, but not uniformly definable in propositional dependence logic. • Modal intuitionistic dependence logic has a connection with modal intuitionistic logic. • Model checking problem for modal intuitionistic dependence logic is PSPACEcomplete.