Implementing Java interfaces: when is it OK to add extra methods?

I have just found myself offended by a usage and I want to write out why.

public interface Stack {
  public int size();
  public boolean isEmpty();
  public Object top()  throws StackEmptyException;    
  public void push (Object element);
  public Object pop()  throws StackEmptyException;   
}

public class ArrayStack implements Stack {

  ......

  public Object atPosition(int i) throws StackOutOfScopeException {
    if (i > tos)
      throw new StackOutOfScopeException("Attempt to pass top of stack");
    else
      return S[i - 1];
  }
}

My claim is that the atPosition should either be in the interface or not in the class, or ArrayStack should be called AugmentedArrayStack or that an intermediate interface called AugmentedStack which extends Stack is needed.

My expectation is that if a class implements only one interface and that interface is named for a Noun and does not have a pertinent name (eg ...Mixin) then the class will only implement methods declared in that interface (and possibly override those inherited from Object).