In addition to being available in the Cornerstone Admin as a live feed, Cornerstone logs are generated in a text file format. They can be opened in a text editor/parser/reader for viewing and analysis. 

Optionally, Cornerstone logs can be sent to a Syslog Server. In short, the benefits of SysLog Servers are that you have a centralized location for errors and logging information for the network. In addition, you have the benefit of a uniform format for all of your logging and errors.
As an example, if an issue occurs at 16:00 - you can have all of the logs from all devices on your network in one location and in the same format - making it much easier to find the incident and determine what occurred.