THE FLC TAXIES ACROSS THE ACTIVE RWY WITHOUT A CLRNC.

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I COMPLETELY MISUNDERSTOOD INFO GIVEN TO ME AS A CLRNC TO FOLLOW ANOTHER ACFT AND CROSS RWY 31R AT MDW. THIS CAUSED A LIGHT TWIN TO GAR. WHEN I REFLECT ON THE RADIO XMISSION FROM GND TO US; I CAN'T IMAGINE WHY I THOUGHT I RECEIVED A CLRNC. PHRASEOLOGY PLAYED A PART IN THE MISUNDERSTANDING ON MY PART. AT ALL TIMES PHRASEOLOGY SHOULD BE SHORT TO THE POINT AND STATED OR ISSUED TO 1 ACFT AT A TIME. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED HE WAS CAPT OF A DC9- 30. HE SAID HE SAW AN AIRPLANE LNDG ON RWY 04 ABOUT THE TIME THE CTLR CLRED THEM TO TAXI TO RWY 22L. HIS 'MINDSET' LOCKED ON TO TAXI TO RWY 04L. AS HE WAS GOING ON THE RWY 31R THE FO CALLED ATTN TO THE LIGHT TWIN GOING AROUND AT THE APCH END OF RWY 31R. THE CAPT WAS TOLD HE HAD CROSSED AN ACTIVE RWY WITHOUT A CLRNC AND TO CONTINUE TO RWY 31C. THE CAPT CONTINUED TO RWY 31C AND FLEW AN UNEVENTFUL FLT TO STL. AT STL THE CAPT CALLED MIDWAY TWR TO APOLOGIZE AND WAS TOLD BY MIDWAY TWR SUPVR THEY SAW WHAT WAS HAPPENING AND SENT THE LIGHT TWIN AROUND. THE SUPVR FURTHER STATED THE TWR PHRASEOLOGY WAS NOT AS CLR AS IT SHOULD HAVE BEEN AND NO FURTHER ACTION WOULD BE TAKEN BY THE TWR AND THANKS FOR CALLING. SUPPLEMENTAL INFO FROM ACN 328162: OUR CLRNC WAS TO WAIT FOR AN ACR B727 TO PASS; THEN TO FOLLOW IT TO RWY 31C; HOLDING SHORT OF RWY 31R. DURING THE WAIT SEVERAL ACFT WERE CLRED TO RWY 22L PROMPTING THE CAPT TO ASK ME TO CONCUR THAT WE WERE GOING TO RWY 31C. I CONCURRED AND WE BEGAN THE TAXI. AS WE APCHED RWY 31R GND CLRED US TO 'TAXI TO RWY 22L.' STILL ROLLING TOWARD RWY 31R; I LOOKED L AND SAW AN ACFT LNDG LIGHT. DUE TO THE DISTORTION OF THE SLIDING WINDOW I COULD NOT TELL WHICH RWY IT WAS ALIGNED WITH OR HOW FAR OUT IT WAS. THE CAPT WAS ADDING PWR TO CROSS WHEN I POINTED IT OUT. THE ACFT WAS ON FINAL FOR RWY 31R AND WAS ISSUED A GAR. GND THEN INFORMED US WE HAD CROSSED AN ACTIVE WITHOUT CLRNC. I BECAME CONFUSED AS TO OUR CLRNC WHEN I SAW THE ACFT ON FINAL APCH. WHEN I POINTED THE TFC OUT TO THE CAPT; MY EXPECTATION WAS THAT HE WOULD STOP EVEN THOUGH WE MIGHT STILL HAVE INTRUDED ON THE RWY. IN RETROSPECT; MY PERCEPTION THAT SOMETHING WAS AMISS SHOULD HAVE RESULTED IN A CHALLENGE TO HIS DECISION TO CROSS. CALLBACK CONVERSATION WITH RPTR OF ACN 328162 REVEALED THE FOLLOWING INFO: THE RPTR STATED HE WAS FO ON A DC9- 30. HE SAID THE CTLR COULD HAVE ALERTED THE CREW TO A CHANGE OF PLANS BY SAYING 'DISREGARD CLRNC TO RWY 31C; MAKE A 110 DEG TURN TO YOUR R AND CLRED TO RWY 22L.' LNDG AT THEIR DEST THE CAPT CALLED MIDWAY TWR. AFTER REVIEWING THE TAPES THE TWR SAID THERE WAS A LOT OF CONFUSION AND THEY WERE NOT GOING TO PURSUE THE ISSUE.