The search for mathematical structures to represent some logics is important for a better understanding of these logics. When we use modalities to generate other logics we need other structures to represent them, as relational frames for normal modal logics. In the case of non-normal modalities, we need neighborhood frames to represent classical modal logics. In this work, we investigate neighborhood frames for non-normal modal logics, with the goal to relate frame semantics with proof systems. Moreover we aim to understand proof systems with semantic language internalized.