Have a matter against any man - Have a complaint of injury; if injustice has been done them by anyone.
The law is open - See the margin. Ἀγόραιοι Agoraioi ἄγονται agontai, that is, ἡμέραι hēmerai. There are court-days; days which are open, or appointed for judicial trials, where such matters can be determined in a proper manner. Perhaps the courts were then held, and the matter might be immediately determined.
And there are deputies - Roman proconsuls. See the notes on Acts 13:7. The cause might be brought before them with the certainty that it would be heard and decided. The Syriac reads this in the singular number “Lo, the proconsul is in the city.”
Let them implead one another - Let them accuse each other in the court. The laws are equal, and impartial justice will be done.