{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-homomorphism-between-fine-and-ferguson-s","title":"An Epimorphism between Fine and Ferguson's Matrices for Angell's AC","arxiv_id":"2105.15160","date":"2021-05-31","proceeding":null,"authors":["Richard Zach"],"abstract":"Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. It is shown that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. Some candidate 7-valued matrices are ruled out as characteristic of AC. Whether matrices with fewer than 9 values exist remains an open question. The results were obtained with the help of the MUltlog system for investigating finite-valued logics; the results serve as an example of the usefulness of techniques from computational algebra in logic. A tableau proof system for NC is also provided.","url_abs":"https://arxiv.org/abs/2105.15160v3","url_pdf":"https://arxiv.org/pdf/2105.15160v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-homomorphism-between-fine-and-ferguson-s","repo_url":"https://github.com/rzach/multlog","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"a-homomorphism-between-fine-and-ferguson-s","repo_url":"https://github.com/rzach/ncac","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}