THERE WAS HVY TRAFFIC AT THE NASHVILLE METRO ARPT WHEN AIR MIDWEST FLT 4530 (SWEARINGEN SA-226TC, N256AM) ARRIVED DRG A MORNING FLT. THE FLT CREW MADE AN ILS APCH TO RWY 31 AS ANOTHER ACFT (AMERICAN FLT 130) WAS ON AN APCH TO RWY 2L. THE 2 RWYS INTERSECTED NR THE MIDPOINT OF RWY 31. THE TWR CTLR CLRD FLT 4530 TO LND ON RWY 31, BUT INSTRUCTED THE FLT CREW TO HOLD SHORT OF RWY 2L. THE FLT REPLIED WITH AN UNINTELLIGIBLE COMMENT FLWD BY '. . . AIR MIDWEST 4530'S CLEARED TO LAND, 31.' THE TWR CTLR EXPECTED THE FLT TO HOLD SHORT OF RWY 2L. HOWEVER, AFTER LNDG, FLT 4530 CONTD ITS LNDG ROLL & CROSSED RWY 2L. THE RWY INCURSION OCCURRED AS FLT 130 WAS LNDG ON RWY 2L. THE CAPT OF FLT 4530 WAS AWARE OF INTERSECT-ING RWY OPNS, BUT SAID THAT BOTH HE & THE 1ST OFFICER UNDERSTOOD THEIR CLNC INCLUDED THE USE OF THE FULL RWY. A CHECK OFTHE TWR TAPES VERIFIED THE CTLR HAD TOLD FLT 4530 TO HOLD SHORT OF RWY 2L; HOWEVER, THE FLT CREW DID NOT ACKNOWLEDGE THAT INSTRUCTION & THE TWR CTLR FAILED TO ASK FOR AN ACKNOWLEDGEMENT.