 The principles of propositional modal logic, found in Prior Analytics I.15, were generally expressed as follows: if the antecedent of a valid consequence is possible/necessary, the consequent is possible/necessary (Abelard, Dialectica 202.6–8). However, the main interest was in modal syllogistic and modal predicate logic. Avicenna (d. 1037) wrote a brief Arabic summary of Aristotle’s modal syllogistic, but his own theory was different, being based on the assumptions that the subject terms and the predicate terms of assertoric and modal propositions stand for all possible applications and the truth-conditions of assertoric propositions and corresponding possibility propositions are the same. It follows, for example, that syllogisms with assertoric premises coincide with uniform possibility syllogisms (Street 2002, 2005; Lagerlund 2009). Avicenna was particularly interested in relative necessities and distinguished between various types of conditional necessities in terms of temporal determinations. Later Arabic works on modal theories were much influenced by Avicenna. (See Strobino and Thom 2016.) While Averroes’s commentaries on the Prior Analytics followed the main lines of Aristotle’s text, his separate treatise on modality involved new systematic ideas, mainly the theory of accidental and per se necessary terms and the interpretation of syllogistic necessity premises as per se necessary predications with per se necessary terms. Both ideas were inspired by Aristotle’s remarks in the Posterior Analytics I.4. Since Averroes took modal premises to be of the divided type, assertoric premises in Aristotelian mixed necessity-assertoric syllogisms must have a predicate term which is necessary. The same applies to the subject term of the first premise in mixed assertoric-necessity syllogisms (Quaesita octo in librum Priorum Analyticorum, IV.3, 84, in Aristotelis Opera cum Averrois Commentariis I.2b; see also Thom 2003, 81–85). This is a speculative explanation of Aristotle’s asymmetric treatment of mixed necessity-assertoric syllogisms and mixed assertoric-necessity syllogisms. Gersonides later tried to develop further Averroes’s remarks; see Manekin 1992. Analogous essentialist ideas were developed in thirteenth-century Latin discussions. 