Research in medieval logic has achieved a point at which it is possible to write an overview of what the undertaking was about that is comprehensive, historically reliable, and congenial to the current academic audience. The aim of this project is to provide one. The monograph will expose the different medieval understandings of what the real phenomena constituting logic were, concentrating on the peak period of the enterprise in the early fourteenth century. The main authors considered are Walter Burley, William Ockham, John Buridan, and Thomas Bradwardine. Particular attention in the research is paid to finding out and making clear whether the mathematical paradigm that has been paramount in modern logic was in the making already in the early fourteenth century. The tangible result of the project is a landmark monograph, whose first draft is to be written during the period at IAS CEU.