{"paper":{"title":"Residuated Basic Logic I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Minghui Ma, Zhe Lin","submitted_at":"2014-02-24T00:52:27Z","abstract_excerpt":"We study the residuated basic logic ($\\mathsf{RBL}$) of residuated basic algebra in which the basic implication of Visser's basic propositional logic ($\\mathsf{BPL}$) is interpreted as the right residual of a non-associative binary operator $\\cdot$ (product). We develop an algebraic system $\\mathsf{S_{RBL}}$ of residuated basic algebra by which we show that $\\mathsf{RBL}$ is a conservative extension of $\\mathsf{BPL}$. We present the sequent formalization $\\mathsf{L_{RBL}}$ of $\\mathsf{S_{RBL}}$ which is an extension of distributive full non-associative Lambek calculus ($\\mathsf{DFNL}$), and sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3354","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"}