The best way to work with checkboxes is to have 2 checkbox elements for each column, one for True and another for False. set the value of the checkbox to be the True or False value that is stored in the DB.
Then in the DataAssist Search wizard, set the search criteria to be a keyword type instead of check type. Again, you will need to add two search criteria for each column, the forst one using the true checkbox for that column, the second one using the false checkox for that column.