Ferrari, Edson Fernando & GPT5mini, Alice: 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.