This could be accomplished by the concept of a "Lease." The Reader is granted, via the Owner, the ability to perform operations on the Data with a set of expiry conditions (time, usage count, etc). See Vanish.
Vanish was achieved by leveraging the BitTorrent DHT to decentralize the storage of data. However, Vanish was proven by a seperate group of researchs to be susceptible to Sybil Attacks ("UnVanish", https://news.utexas.edu/2009/09/29/new-digital-security-program-doesnt-protect-as-promised)
I believe that, leveraging, zk-SNARKS, one could feasibly execute arbitrary computation (via a contract) upon data without ever knowing the target data. This would be valuable for the Owner because they could allow the Reader (social networks, advertising networks, peers, untrusted parties, etc) to access data for a teporray amount of time without the Reader having the ability to replicate or otherwise copy the data, in plain, off the encrypted viewing volume while still allowing the Reader to verify that they have access to the actual data.
- Pattern matching using ML
- Reputation systems