A B737 TAXIES AT MDW; IL; AND HAS A RWY INCURSION AT RWY 31R.

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AFTER PUSHBACK FROM GATE XX AT MDW; WE WERE ACCOMPLISHING THE AFTER START CHKS AND CALLED GND FOR TAXI. WE WERE CLRED TO TAXI TO THE ACTIVE (RWY 31C). UPON START OF TAXI; I ASKED THE FO IF WE WERE CLRED TO CROSS RWY 31R. HE ANSWERED 'NO I THINK HE SAID TO HOLD SHORT OF THE R.' I THEN SAID I'M SURE HE SAID TO CROSS THE R; LOOKED AND DIDN'T SEE ANY TFC AND STARTED ACROSS THE RWY 31R. AS WE WERE XING THE R RWY THE GND CTLR QUICKLY STATED 'CALL SIGN; THE CALL WAS HOLD SHORT OF RWY 31R; EXPEDITE ACROSS TO RWY 31C TFC ON FINAL FOR THE R.' AT THAT TIME I LOOKED AGAIN AND SAW A LIGHT SINGLE ON ABOUT A 1 1/2 MI FINAL FOR THE R RWY. THERE WERE NO EVASIVE ACTIONS OR CONFLICTS BY ANY ACFT. WE CROSSED AND CONTINUED FOR TKOF. I THINK WHAT MADE THIS SIT CONFUSING WAS THE CLRNC TO TAXI TO THE CTR RWY FOLLOWED BY THE INSTRUCTION TO HOLD SHORT OF THE CLOSER; R RWY. IF THE CLRNC HAD BEEN GIVEN TO HOLD SHORT OF THE R FIRST FOR TAXI TO THE CTR RWY; I MAY NOT HAVE MISTAKENLY THOUGHT I WAS CLRED TO THE ACTIVE AND CROSSED THE R. SUPPLEMENTAL INFO FROM ACN 383860: WE STARTED OUR SHORT TAXI (APPROX 200 FT) AND THE CAPT ASKED ME IF WE WERE CLRED TO CROSS RWY 31R. I TOLD HIM I THOUGHT THE CLRNC INCLUDED 'HOLD SHORT' OF RWY 31R; AND HE SAID HE THOUGHT IT WAS TO CROSS RWY 31R TO RWY 31C. AS WE WERE XING RWY 31R; GND CALLED AND SAID THE CLRNC WAS 'TO HOLD SHORT OF RWY 31R; CONTINUE TO CROSS RWY 31R; TFC ON FINAL.' WE CONTINUED TO CROSS AND HOLD SHORT OF RWY 31C. WE SAW TFC ON FINAL RWY 31R AFTER WE CROSSED. NO EVASIVE ACTION WAS REQUIRED BY US OR THE CESSNA ON FINAL. I THINK THE PROB WAS THAT WE'RE USUALLY CLRED 'CLRED TO CROSS RWY 31R TAXI TO RWY 31C.' AND THIS TIME WE WERE CLRED 'TO TAXI TO RWY 31C; HOLD SHORT OF RWY 31R.' THIS CREATED THE CONFUSION; AND ADDED WITH THE SHORT TAXI AND MY CHKLIST DUTIES CREATED THE POSSIBLE INCURSION.