Sure we can call it “read/ clear notifications”
Basically we need to introduce a concept of scopes, this is how I would lay it out:
id name description (localizable)
-- --------- -----------
1 notification_edit Read / clear notifications
2 user_info Read private user info
3 message_bus Recieve updates from site
permissions
id controller action type
-- ------- ----- ----
1 notifications get :get
etc...