Aristotelian logic was the basis for various traditions of medieval logic: Greek, Armenian, Syriac, Latin, Arabic, and Hebrew. This chapter will concentrate on just two, the Latin and the Arabic. They are certainly the two great traditions of logic in the Middle Ages and the very different ways in which they use the ancient heritage makes a fascinating comparison. A fuller discussion would certainly include the other four traditions: they are omitted here, not just due to considerations of space, but also because scholarship in these areas has not yet reached the stage to make a survey possible.