I believe all VPN providers do keep logs.Maybe the best public vpn out there with perfect-privacy vpn. The only two providers where i am pretty sure they dont log User activitis. One reason for me to use airvpn is the open source client. The Guys behind airvpn are honest and have good knowlagende about what they are doing. One of the rare softwares i do not Change.
The question is whether are they keeping browsing logs or network logs. Browsing logs are extremely personal and private to users, which are not maintained if the provider is serious about users' privacy.
Network Logs (Also known as Troubleshooting, Maintenance, Speed, or Connectivity Logs).
Network logs, on the other hand, are created and maintained to troubleshoot and optimize a service. These logs contain no traces of browsing habits or other private user activities. These logs, among other system logs such as bandwidth consumed, contain mostly the user timestamps.
However, timestamps associate with IP address, connection initiation and disconnection from the VPN providers servers.
So, go figure out whether you can be traceable. From below
To confirm someone’s real IP, two different set of Network Logs are required: one from the VPN provider and the other from the server where the IP visited, browsed or downloaded something. Any one set of Network Logs on its own is pretty much useless since it contains no valuable information. The two must be compared and verified for any link to be confirmed.