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The ability to think about non-actual possibilities is crucial for rational decision and action. When deciding what to do in situations of uncertainty or risk, we use our powers of imagination and conception to surveil the ways the world might be for all we know, and ponder the possible consequences of our actions. What is the logic of conceivability? Do thinking and imagining exhibit sufficient structure so to be amenable to precise modeling? Under what conditions does an imaginative episode establish a non-actual scenario as a real possibility? What are the special features of thought, talk and knowledge about mere possibility and conditionality? The aim of this conference is to facilitate the conversation on these questions by bringing together both senior and rising young researchers from around the world.