ACR X TKOF ON MULTIPLE RWY OP INTERSECTING RWYS HAD LTSS FROM ACR Y. SYS ERROR.

Narrative

ACR X WAS CLRED INTO POS AND HOLD ON RWY 9 AT BOSTON LOGAN. TWR WAS HANDLING TFC ON RWYS 9 AND 4R. TFC WAS LNDG RWY 4L AND 4R. ACFT WAS CLRED FOR TKOF; CAPT WAS FLYING; FO COMPLETED CHKLIST. AS BRAKES WERE RELEASED; I (CAPT FLYING) SAW ACR Y ON TKOF ROLL ON RWY 4R. I STOPPED THE ACFT AND QUERIED THE TWR IF WE WERE STILL CLRED FOR TKOF. THE TWR ANSWERED 'ROGER.' THE TWR HAD ANSWERED THE FO'S INITIAL CLRED FOR TKOF AND MINE WHILE ACR Y WAS STILL ON TKOF ROLL. AFTER ACR Y DEPARTED; WE COMPLETED A NORMAL TKOF. I CALLED BOS TWR AND SPOKE TO THE TRACON MGR AND EXPLAINED WHAT HAD HAPPENED. HE SAID IF THE TWR THOUGHT WE WOULD HAVE ADEQUATE SEPARATION; HE CAN CLR BOTH ACFT FOR TKOF. HE ASKED ME IF I THOUGHT WE HAD ADEQUATE SEPARATION. I EXPLAINED THAT IF I DID NOT STOP; THERE WOULD HAVE BEEN A COLLISION SINCE THE JET WAS ALREADY ON TKOF ROLL. I BELIEVE THAT WITH ALL THE ACTIVITY AT BOS THAT THE TWR THOUGHT WE WOULD HAVE SEPARATION; BUT DID NOT CONFIRM IT OR TAKE NOTICE OF THE PROX OF THE 2 ACFT. THIS IS A POTENTIALLY HAZARDOUS SIT; ESPECIALLY ON LOW VISIBILITY DAYS.