MULTIPLE RWY OP INTERSECTING RWYS SMA X TKOF HAD NMAC WITH SMA ON GAR. SEE AND AVOID CONCEPT.

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SMA X ON A TRAINING FLT. I WAS THE INSTRUCTOR. REPUBLIC ARPT WAS USING INTERSECTING RWY OPS (RWY 1 FOR DEPS AND RWY 32 FOR LNDG). WE WERE CLRED FOR TKOF. AS OUR ACFT BECAME AIRBORNE; I SAW SMA Y AT APPROX 2 O'CLOCK CONVERGING AND CLBING OUT. I IMMEDIATELY TOOK CTL OF THE ACFT AND MANEUVERED TO AVOID A COLLISION OVER THE RWY INTXN. I DID NOT RECEIVE ANY WARNING FROM TWR OR OTHER PLT OF HIS/HER DECISION TO ABORT THE LNDG. AFTER THE INCIDENT AND DISCUSSIONS WITH TWR SUPVR; HE CLAIMS THAT THE OTHER PLT HAD ACKNOWLEDGED THE CLRNC TO LAND AND HOLD SHORT. THEREFORE; HE HAD NO RIGHT TO EXECUTE A GAR. IT IS MY OPINION THAT EVEN WITH A CLRNC TO 'HOLD SHORT;' THE PLT SHOULD HAVE THE OPTION TO EXECUTE A GAR. THE TWR CTLR MUST NOT PERMIT (AUTHORIZE) A TKOF WITH AN ACFT ON SHORT FINAL OR IN THE LNDG ROLL UNTIL THE ACFT HAS REACHED A TAXI SPD. ACCORDING TO TWR PERSONNEL AND SUPVR; ONCE A PLT HAS ACCEPTED A 'CLR TO LAND AND HOLD SHORT' CLRNC; THEY WILL ASSUME THAT THE PLT WILL NOT CROSS THE OTHER RWY.