ACFT TAXIED NEAR RWY WHICH CAUSED TWR TO CANCEL ANOTHER ACFT'S TKOF CLRNC.

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PUSHED OUT OF GATE AT MDW. STARTED ENGS AND CALLED READY TO TAXI. LNDG AND DEPARTING RWYS 31. TAXI INSTRUCTIONS WERE GIVEN TO TAXI: TXWY P; TXWY G SHORT OF RWY 31R. I HAD LOOKED AT THE 10-9 PAGE AND IT APPEARED THAT THE RAMP AREA WAS TXWY Y; AND I SAW TXWY P TO THE N. AS WE TAXIED STRAIGHT AHEAD; I SAW TXWY P; WHICH SEEMED TO GO MORE STRAIGHT AHEAD RATHER THAN MAKING A SHARP R TURN AS IT APPEARS ON THE 10-9 PAGE. FROM OUR CLRNC I ASSUMED IT WAS OK TO CROSS ALL OTHER RWYS AND HOLD SHORT OF RWY 31. SO WHILE I WAS TAXIING I STARTED TO GO ON TXWY P STRAIGHT AHEAD AND WAS LOOKING ACROSS RWY 22L FOR A TXWY G. ALL ABOUT THE SAME INSTANT WHEN I REALIZED THERE WASN'T A TXWY G ACROSS THE WAY; I CLRED L AND R AND SAW AN ACFT WITH ITS LIGHTS ON AND THE RWY 22L RWY SIGN AND STARTED TO STOP. AT THE SAME TIME; MDW GND SAID 'ACR X STOP.' DURING THIS TIME I BELIEVE THE ACFT ON RWY 22L HAD JUST STARTED HIS TKOF ROLL AND WAS TOLD TO STOP BY THE TWR. WE WERE STILL ON GND CTL AND WE DIDN'T HEAR ANYTHING SAID ON TWR FREQ. I WAS ALSO SURPRISED AN ACFT WAS DEPARTING ON RWY 22L. WE TAXIED TO RWY 31C AND TOOK OFF. I CALLED BACK TO MDW INFLT AND TALKED TO A SUPVR AND APOLOGIZED FOR THE PROB AND ASSURED HIM WE WERE WELL SHORT OF RWY 22L. HE SAID HE WAS HAPPY THE SYS WORKED AND EVERYTHING WAS FINE AND HE FELT THERE WAS NO RWY INCURSION.