{"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/solving-tree-problems-with-category-theory","title":"Solving Tree Problems with Category Theory","arxiv_id":"1810.07307","date":"2018-10-16","proceeding":null,"authors":["Rafik Hadfi"],"abstract":"Artificial Intelligence (AI) has long pursued models, theories, and\ntechniques to imbue machines with human-like general intelligence. Yet even the\ncurrently predominant data-driven approaches in AI seem to be lacking humans'\nunique ability to solve wide ranges of problems. This situation begs the\nquestion of the existence of principles that underlie general problem-solving\ncapabilities. We approach this question through the mathematical formulation of\nanalogies across different problems and solutions. We focus in particular on\nproblems that could be represented as tree-like structures. Most importantly,\nwe adopt a category-theoretic approach in formalising tree problems as\ncategories, and in proving the existence of equivalences across apparently\nunrelated problem domains. We prove the existence of a functor between the\ncategory of tree problems and the category of solutions. We also provide a\nweaker version of the functor by quantifying equivalences of problem categories\nusing a metric on tree problems.","url_abs":"http://arxiv.org/abs/1810.07307v1","url_pdf":"http://arxiv.org/pdf/1810.07307v1.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":"abstracts"},"code_links":[{"paper_slug":"solving-tree-problems-with-category-theory","repo_url":"https://github.com/raviq/tree_algebra","is_official":1,"mentioned_in_paper":0,"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}