I tried the following in the IE debugger console;
>>localStorage["Dave"] = "Dave";
"Dave"
>>localStorage.Aproperty = "Dave";
"Dave"
>>localStorage["Dave"];
"Dave"
>>localStorage.Aproperty
"Dave"
>>localStorage.clear();
undefined
>>localStorage.Aproperty;
undefined
>>localStorage["Dave"];
undefined
works as expected..........
I know that this isn't an Answer, but it wouldn't look right as a comment.