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Possibility Relations and General Modal Semantics
We introduce a general modal semantics based on a primitive possibility relation \[ P \subseteq W \times \mathcal P(W), \] where \(P(w,U)\) means that the proposition \(U\) is possible at \(w\). Kripke semantics arises as a particular case, and neighborhood semantics is recovered by duality. The resulting formulation is technically simpler and directly possibility-theoretic.
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