Intermediate Logics in the Setting of Team Semantics

Several authors have recently defined intuitionistic logic based on team semantics ( \(\textsf{tIPC}\) ). In this paper we provide two alternative approaches to intermediate logics in the team semantics setting. We do this by modifying \(\textsf{tIPC}\) with axioms written with two different versions of disjunction in the logic, a local one and global one. We prove a characterization theorem in the first approach and we introduce a generalized team semantics in the second one.