Virtually all characteristics that are applied as to an assault rifle fall apart on details.
It need not be an intermediate caliber because other rifles in a "rifle caliber" (but not an intermediate cartridge) share all the characteristics. Or at least one did.
It need not be able to be fitted with a bayonet. The original Stg44 (MP44) did not, nor did the first AK-47s.
Some bolt action rifles were fitted with high capacity (more than 10 rounds) as far back as WWI but I suppose no one would all such a thing an assault rifle, even is they were used by real "storm troopers," who by then were unlikely to be wearing jackboots.
Any cartridge fired by a semi-automatic rifle has exactly the same destructive power as the same cartridge fired by a full-auto rifle.
Still, some trivialities have escaped precise definition. Is an M1 carbine an assault rifle? If not, what about an M2? True, it has no pistol grip in the current sense of the term but it is select fire. Is a .30 carbine cartridge an intermediate cartridge? Or does it fall beneath some defined floor? The M2 took a bayonet, if that helps, point-wise.
Then there's the Browning Automatic Rifle, which has everything but black plastic (neither did .30 carbines)--except the intermediate cartridge. Oh, and no pistol grip, either. It loses on points but because of the full power cartridge, you might call it an assaut and battery rifle.
Well, what about sub-machine guns. Might they be called sub-assault rifles? They pretty much have everything except the full-intermediate cartridge. Some even take bayonets but surprisingly few have black plastic stocks.
Finally, what about the current army version of the old, old, old M-16 (it's been used for well over 40 years)? Yes, it's select fire, sort of, only it isn't what you would call full-auto. Where does burst fire fit into this equation? We may have to rethink this whole business.
Shoot low, sheriff. They're riding Shetlands!
Underneath the starry flag, civilize 'em with a Krag,
and return us to our own beloved homes!
Buy War Bonds.