A logical vulnerability is a vulnerability that doesn't require memory corruption to be executed. Instead, it abuses the application logic to perform unintended actions. A good example of this is CVE-2010-2729 (MS10-061), named Windows Print Spooler Service Vulnerability, which is used by Stuxnet malware. Let's dig deeper into how it works.
Windows printing APIs allow the user to choose the directory that he or she wishes to copy the file to be printed to. So, with an API named GetSpoolFileHandle, the attacker can get the file handle of the newly created file on the target machine and then easily write any data there with the WriteFile (or similar) API. A vulnerability like this one targets the application logic, which allows the attacker to choose the directory they wish and provides them with the file handle to overwrite this file with any data he or she wants.
Different logical vulnerabilities are possible, and there is no specific format for them...