{"paper":{"title":"Multi-sorted logic, models and logical geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Aleko Gvaramia, Boris Plotkin, Elena Aladova, Tatjana Plotkin","submitted_at":"2015-06-18T19:47:45Z","abstract_excerpt":"Let $\\Theta$ be a variety of algebras, $(H, \\Psi, f)$ be a model, where $H$ is an algebra from $\\Theta$, $\\Psi$ is a set of relation symbols $\\varphi$, $f$ is an interpretation of all $\\varphi$ in $H$. Let $X^0$ be an infinite set of variables, $\\Gamma$ be a collection of all finite subsets in $X^0$ (collection of sorts), $\\widetilde\\Phi$ be the multi-sorted algebra of formulas. These data define a knowledge base $KB(H,\\Psi, f)$. In the paper the notion of isomorphism of knowledge bases is considered. We give sufficient conditions which provide isomorphism of knowledge bases. We also study the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06057","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"}