When the XOr has two inputs, it performs a logical operation that outputs a signal only when both inputs differ (one input has a signal, the other is No signal).  In other words the output is a signal if the inputs are not alike, otherwise the output is false.  A way to remember XOR is “one or the other, but not both”.
When the XOr has three or more inputs, the logical result outputs a signal when the number of signals at the inputs is odd, and no output signal when the number of input signals is even.

Note: Long and Short are calculated separately in BloodHound. I.e. In the example of an XOr, if you have two solvers connected and one is producing a Long Signal and the other is producing a Short Signal, this will result in a signal in both directions. See: https://www.sharkindicators.com/documentation/bloodhound-reference/#bloodhound-output