Iterated team semantics for a hierarchy of informational types

Abstract

In this paper, we introduce and study a framework that is inspired by the team semantics for propositional dependence logic but deviates from it in several respects. Most importantly, instead of the two semantic layers used in dependence logic – possible worlds and teams – a whole hierarchy of contexts is introduced and different types of formulas are evaluated at different levels of this hierarchy. This leads to a rich stratification of informational types. In this framework, the dependence operator of dependence logic can be defined by the standard propositional connectives (negation, conjunction, disjunction and implication). We explore the formal aspects of this approach and apply it to a number of puzzling phenomena related to modalities and conditionals.