In this paper I shall be concerned with the notion of logical consequence in the tradition of Arabic logic. In particular I shall look at how one of the central figures in the history of Arabic logic, Ibn Sīnā (d. 1037), deals with this topic and discuss how his idea of what it is for something to follow from something else is related to an elaborate account of modality and grounded in the more general framework of his theory of predicables. The focus of my analysis will be on various accounts of inseparability and the way in which they yield progressively stronger notions of logical consequence. In doing so, connections with earlier (Al-Fārābī, d. 950) and later (Post-Avicennan logicians until the XIIIth century) developments will be also sketched.