Intentions are crucial for our practical reasoning. The rational intention obeys some simple logical principles, such as agglomeration and consistency, among others, motivating the search for a proper logic of intention. However, such a logic should be weak enough not to force the closure under entailment; otherwise, we cannot distinguish between intended consequences of agents' choices and their unintended side-effects. In this paper we argue that we should avoid not only the closure under entailment, but the weaker closure under equivalence as well. To achieve this, we develop a hyperintensional logic of intention, where what an agent intends is constrained by the agent's decision problem. The proposed system combines some elements of inquisitive and topic-sensitive theories of intensional modals. Along the way, we also show that the existing closest relatives of our framework overgenerate validities by validating some instances of closure under equivalence. Finally, we provide a sound and strongly complete axiomatization for this logic.
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