Should one interface inherit another interface

Consider whether the interfaces should be logically paired, and if you feel that they work well with each other then absolutely use inheritance.

Lets look at an example;

public interface IScanner
{
    void Scan();
}

public interface IPrinter
{
    void Print();
}

Printers and scanners are often separate objects, each with their own functionality however these two devices are often paired in the same device;

public interface IPhotocopier : IScanner, IPrinter
{
    void Copy();
}

It makes sense that IPhotocopier should inherit from IScanner and IPrinter as this now allows the photocopier to be used as either a scanner or printer (which it contains) in addition to its primary roll as a copier.

Now lets look at one more interface;

public interface IBlender
{
    void Blend();
}

It would not make sense to allow IBlender to be inherited by any of the earlier interfaces (what would you call them? IBlendingScanner?).

If you can't give your new interface a sensible name this might indicate that your may not want to use inheritance in this instance.

It's a bad idea to inherit some interfaces such as IDisposable, since this forces all implementations of your new interface to implement the dispose pattern even if they do not have any disposable resources.

Interface inheritance is an excellent tool, though you should only use it when interface B is truly substitutable for interface A, not just to aggregate loosely-related behaviors.

It's difficult to tell whether it is appropriate for your specific case, but there's nothing wrong using the practice in principle. You see it in the first-rate APIs all the time. To pick just one common example, from the .NET framework:

public interface ICollection<T> : IEnumerable<T>, IEnumerable