Which branch of philosophy that deal with arguments​

Logic

logic originally meaning the word, or what is spoken, but coming to mean thought or reason is most often said to be the study of arguments.

citizens were able to charge more for their goods and services

male citizens in athens could vote on all the decisions that affected the city and serve on juries. however, democracy was not open to everyone. citizen women and children were not allowed to vote. slaves and foreigners living in athens (known as metics) were banned from participating in government.