{"paper":{"title":"Pointwise intersection in neighbourhood modal logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dominik Klein, Frederik Van De Putte","submitted_at":"2018-04-26T21:38:21Z","abstract_excerpt":"We study the logic of neighbourhood models with pointwise intersection, as a means to characterize multi-modal logics. Pointwise intersection takes us from a set of neighbourhood sets $\\mathcal{N}_i$ (one for each member $i$ of a set $G$, used to interpret the modality $\\square_i$) to a new neighbourhood set $\\mathcal{N}_G$, which in turn allows us to interpret the operator $\\square_G$. Here, $X$ is in the neighbourhood for $G$ if and only if $X$ equals the intersection of some $\\mathcal{Y} = \\{Y_i \\mid i\\in G\\}$. We show that the notion of pointwise intersection has various applications in ep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10285","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}