Fine-grained modal logics: a simple approach

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A logic is fine-grained (or hyperintensional) if valid equivalence is not a congruence relation on the set of formulas. Such logics are studied by philosophical logicians at least since the 1970s (Cresswell) and they rose to prominence once again in recent work by Fine, Berto, Leitgeb and others. We present a simple yet fairly general framework for fine-grained extensions of normal modal logics and show how the framework relates to some recent approaches.