EXCLUSIVE

Several private citizens were instrumental in cornering cop killer Christopher Dorner ... but there may be a gigantic loophole preventing any of them from collecting the loot.

There are 3 rewards. The Mayor of L.A. announced a $1 million reward -- funded by private groups -- for information leading to the "capture and conviction" of Dorner. Big problem -- technically speaking, Dorner must be both captured AND convicted to trigger the reward.

The L.A. City Council offered a $100,000 reward for information leading to "the identification, apprehension, and conviction" of Dorner. Again ... no conviction. City Council sources tell us there's already a disagreement between the Legislative Analyst and the City Attorney over how to interpret the reward language.

And finally ... the L.A. County Board of Supervisors offered a $100,000 reward for information ""Dorner was cornered but not captured." And finally ... the L.A. County Board of Supervisors offered a $100,000 reward for information " leading to the capture of Christopher Dorner." One source at the Board of Supervisors tells TMZ,"Dorner was cornered but not captured."