{"paper":{"title":"The Lattice of Congruences of a Finite Line Frame","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Carlos Areces, Daniel Penazzi, Miguel Campercholi, Pedro S\\'anchez Terraf","submitted_at":"2015-04-08T00:18:00Z","abstract_excerpt":"Let $\\mathbf{F}=\\left\\langle F,R\\right\\rangle $ be a finite Kripke frame. A congruence of $\\mathbf{F}$ is a bisimulation of $\\mathbf{F}$ that is also an equivalence relation on F. The set of all congruences of $\\mathbf{F}$ is a lattice under the inclusion ordering. In this article we investigate this lattice in the case that $\\mathbf{F}$ is a finite line frame. We give concrete descriptions of the join and meet of two congruences with a nontrivial upper bound. Through these descriptions we show that for every nontrivial congruence $\\rho$, the interval $[\\mathrm{Id_{F},\\rho]}$ embeds into the l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01789","kind":"arxiv","version":2},"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"}