Axiomatizing the Logic of Imagination

In a recent paper Berto introduces a semantic system for a logic of\r\nimagination, intended as positive conceivability, and aboutness of imaginative\r\nacts. This system crucially adopts elements of both the semantics\r\nof conditionals and the semantics of analytical implications in order to\r\naccount for the central logical traits of the notion of truth in an act of\r\nimagination based on an explicit input. The main problem left unsolved\r\nis to put forward a complete set of axioms for the proposed system. In the\r\npresent paper I offer a solution to this problem by providing a complete\r\naxiomatization of a generalization of the original semantics. The difficulty\r\nin proving completeness lies in the fact that the modalities that capture\r\nthe notion of truth in an act of imagination are neither standard nor minimal,\r\nso that the construction of the canonical model and the proof of the\r\ntruth lemma are to be substantially modified.