Someone knows that local reasoning on hypergraphs is a weakly aggregative modal logic

Epistemic Logics of Structured Intensional Groups

“…This will allow us to adapt and apply the well understood model theory of monotone neighborhood frames (for which we mainly refer to [7,8,14]) to study, among others, algebraic duality or modal definability on a convenient level of abstraction. A similar perspective has recently been adopted also by [3] on a logic containing a somebody-knows modality, previously studied by [1]. Neither of the approaches in [7,3] however includes both ∃∀ and ∀∀ types of modalities, and therefore similar modifications of the general theory as those adopted in [2] are necessary, and the algebraic structure underlying the labelling of groups needs to be captured additionally.…”

“…A similar perspective has recently been adopted also by [3] on a logic containing a somebody-knows modality, previously studied by [1]. Neither of the approaches in [7,3] however includes both ∃∀ and ∀∀ types of modalities, and therefore similar modifications of the general theory as those adopted in [2] are necessary, and the algebraic structure underlying the labelling of groups needs to be captured additionally.…”

“…Distributed or common knowledge for intensional group names has also been studied by [12,13]. A monotone neighborhood perspective has recently been adopted by [3] and applied to a logic containing the somebody-knows modality of [1]. Humml and Schröder [9] generalize Grove and Halpern's approach to structured names represented by formulas defining group membership, including e.g.…”