If the use is not specified in the lease, then the issue is:1) If you are renting the entire premises, including the basement--e.g. renting the entirety of a single family home--then you may not be denied use of the basement; you are paying rent for its use and possession.2) If you are only paying rent for part of the premises (e.g. one apartment), then you do not necessarily have access to or use of the basement, except to the degree there was some agreement giving you access or use.