ACR LTT MAKES A MISSED APCH WHEN THE CIRCLING APCH IS NOT COMPLETED.

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DURING OUR DSCNT; MY FO GOT THE ATIS AND TOLD ME BOS WAS LNDG ILS 4R. WE THEN WERE TOLD TO EXPECT ILS 4R TRANSITION TO 4L. SO WE SET UP THE RADIOS ACCORDINGLY. THEN; AFTER NUMEROUS VECTORS FROM BOS APCH; WE WERE GIVEN AN ALT AND HDG TO INTERCEPT THE 15R LOC CIRCLE TO LAND 4L. AT THIS TIME WE WERE ABOUT 5 DME FROM BOS ARPT. HE (APCH) ALSO TOLD US TO CALL THE FIELD IN SIGHT. SO THEN WE SET OUR RADIOS UP FOR 15R ILS AND BEGAN TO TRACK INBOUND. THEN I NOTICED THAT THE EFIS DIDN'T HAVE ENOUGH TIME TO CAPTURE THE GS AND WE GOT A GS FLAG. I THEN BEGAN A DSCNT WHEN THE GS STARTED TO CAPTURE. THEN AT APPROX. 2000 FT AGL WE POPPED OUT OF THE CLOUDS AND DIRECTLY BELOW US WAS BOS LOGAN INTL. WE CALLED THE TWR AND TOLD THEM WE HAD THE ARPT IN SIGHT. HE IMMEDIATELY GAVE US A CLB AND HANDED US OVER TO DEP. WE GOT VECTORED FOR 4R AND LANDED SAFELY. AFTER CLRING THE RWY; WE WERE TOLD TO CALL THE TWR SUPVR; WHICH I DID. HE WANTED TO KNOW WHY WE WERE OVER THE FIELD AT 1500 FT AND NOT TALKING TO ANYONE. I TOLD HIM WHAT OUR INITIAL CLRNC WAS; AND THEY (APCH) CHANGED IT WITHOUT TELLING US (I.E. RWY 15R ILS INSTEAD OF 4R ILS). THEY ALSO FORGOT TO TELL US TO GO TO TWR UNTIL IT WAS TOO LATE. BETTER COM BTWN BOS APCH AND US WOULD NEVER HAVE LET THIS HAPPEN; IT COULD HAVE BEEN MUCH WORSE.