One major fault line in foundational theories of cognition is between the so-called “representational” and “non-representational” theories. Is it possible to formulate an intermediate approach for a foundational theory of cognition by defining a conception of representation that may bridge the fault line? Such an account of representation, as well as an account of correspondence semantics, is offered here. The account extends previously developed agent-based pragmatic theories of semantic information, where meaning of an information state is defined by its interface role, to a theory that accommodates a notion of representation and correspondence semantics. It is argued that the account can be used to develop an intermediate approach to cognition, by showing that the major sources of tension between “representational” and “non-representational” theories may be eased.