B1900 FLT CREW HAS RWY INCURSION ON RWY 4L BOS.

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I WAS HOLDING SHORT OF RWY 4L AT BOS. TWR CTL INSTRUCTED US TO POS AND HOLD ON RWY 4L. I TAXIED AND POS THE ACFT ON RWY 4L. IT WAS THE FO'S LEG; SO I XFERRED THE CTLS OVER TO HIM ONCE POSITIONED ON THE RWY. AFTER I XFERRED THE CTLS; I WENT ON THE PA TO MAKE A BRIEF PAX ANNOUNCEMENT. AS I WAS BRIEFING THE PAX; I HEARD A TKOF CLRNC. I NOTICED THE FO ADVANCING THE PWR LEVERS AND THE ACFT STARTED ROLLING. I QUICKLY FINISHED THE PAX BRIEF AND TURNED ON THE EXTERNAL LIGHTS. AS THE ACFT WAS ROLLING; TWR INSTRUCTED US TO STOP THE ROLL. I IMMEDIATELY TOOK CTL OF THE ACFT AND CAME TO A STOP. THE ACFT SPD AT THE TIME I STOPPED WAS SOMEWHERE BELOW 60 KTS. TWR INSTRUCTED US TO MAKE A 180 DEG TURN TO REPOS AND HOLD ON RWY 4L. I THEN REQUESTED TO EXIT OFF THE RWY INSTEAD. I EXITED OFF AND HELD SHORT OF RWY 4L ONCE AGAIN. I THEN INFORMED TWR WE WERE READY FOR DEP. WE WERE THEN INSTRUCTED TO POS AND HOLD RWY 4L. I POSITIONED THE ACFT ON THE RWY AND XFERRED THE CTLS TO THE FO. A DEP CLRNC WAS GIVEN WHICH I REPEATED AND WE DEPARTED BOSTON. AS WE WERE ON THE INITIAL TKOF ROLL; I BELIEVE THERE WAS AN ACFT ABOUT TO CROSS THE DEP END OF THE RWY. THIS RWY INCURSION WAS PREVENTED WHEN I WAS ASKED TO STOP THE TKOF ROLL BY TWR CTL. LOOKING BACK; I AM NOT SURE IF THE DEP CLRNC WAS GIVEN TO US. WHEN I WAS BRIEFING THE PAX; MY ATTN WAS ON THE PAX. AS I NOTICED THE FO ADVANCING THE PWR LEVERS; I ASSUME THAT HE RECEIVED A TKOF CLRNC AND THAT'S WHY HE STARTED APPLYING TKOF PWR AND INITIATED THE TKOF ROLL. SUPPLEMENTAL INFO FROM ACN 699063: ON RWY 4L; WHILE XING THE HOLD SHORT LINE; THE CAPT IMPLIED THAT HE WAS 'GOING TO THE BACK;' IN OTHER WORDS TO TALK ON THE PA TO BRIEF THE PAX. THE CAPT WAS TAXIING ONTO THE RWY WHILE TALKING ON THE PA. UPON STOPPING THE ACFT ON THE RWY; HE STATED 'YOUR BRAKES -- YOUR CTLS.' I THEN STATED 'MY CTLS.' AT THAT TIME IT WAS MY UNDERSTANDING THAT WE WERE CLRED FOR TKOF AND I ADVANCED THE PWR LEVERS TO INITIATE TKOF ROLL. THE CAPT TURNED ON THE NECESSARY EXTERIOR LIGHTS; AND STATED 'EXTERIOR LIGHTS ON; BEFORE TKOF CHKLIST COMPLETE.' AFTER REACHING 40 KTS DURING TKOF ROLL ON RWY 4L; THE TWR CTLR STATED; 'CALL SIGN; EMER. STOP ON RWY.'