Abstract. This paper connects the following three apparently unrelated topics: an epistemic framework fighting logical omniscience, a class of generalized graphs without the arities of relations, and a family of nonnormal modal logic rejecting the aggregative axiom. Through neighborhood frames as their meeting point, we show that, among many completeness results obtained in this paper, the limit of a family of weakly aggregative logics is both exactly the modal logic of hypergraphs and also the epistemic logic of local reasoning with veracity and positive introspection, which also answers a question left open by Fagin and Halpern (1988). The logics studied are shown to be decidable based on a filtration construction.