{"paper":{"title":"Monotonic Distributive Semilattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ma. Paula Mench\\'on, Sergio A. Celani","submitted_at":"2018-10-19T17:01:54Z","abstract_excerpt":"In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the $\\{\\rightarrow,\\wedge,\\top\\}$-fragment of intuitionistic logic is the variety of implicative meet-semilattices \\cite{CelaniImplicative} \\cite{ChajdaHalasKuhr}. In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator $m$. We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08585","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"}