{"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/mathematical-foundations-for-a-compositional","title":"Mathematical Foundations for a Compositional Distributional Model of Meaning","arxiv_id":"1003.4394","date":"2010-03-23","proceeding":null,"authors":["Bob Coecke","Mehrnoosh Sadrzadeh","Stephen Clark"],"abstract":"We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by Lambek. This mathematical framework enables us to compute the meaning of a well-typed sentence from the meanings of its constituents. Concretely, the type reductions of Pregroups are `lifted' to morphisms in a category, a procedure that transforms meanings of constituents into a meaning of the (well-typed) whole. Importantly, meanings of whole sentences live in a single space, independent of the grammatical structure of the sentence. Hence the inner-product can be used to compare meanings of arbitrary sentences, as it is for comparing the meanings of words in the distributional model. The mathematical structure we employ admits a purely diagrammatic calculus which exposes how the information flows between the words in a sentence in order to make up the meaning of the whole sentence. A variation of our `categorical model' which involves constraining the scalars of the vector spaces to the semiring of Booleans results in a Montague-style Boolean-valued semantics.","url_abs":"https://arxiv.org/abs/1003.4394v1","url_pdf":"https://arxiv.org/pdf/1003.4394v1.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":"mathematical-foundations-for-a-compositional","repo_url":"https://github.com/ICHEC/QNLP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"mathematical-foundations-for-a-compositional","repo_url":"https://github.com/toumix/discopy","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[{"task_slug":"sentence","task_name":"Sentence"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1003.4394","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1003.4394"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/ICHEC/QNLP","reach":{"status":"ok","spdx":"Apache-2.0"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/toumix/discopy","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"summary":{"unverified":1},"by_repo_kind":{"listed":{"samples":1,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"07772773cec85979","entry":"str_delayed","repo":"toumix/discopy","repo_kind":"listed","path":"discopy/feedback.py","file_url":"https://github.com/toumix/discopy/blob/HEAD/discopy/feedback.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"07772773cec85979"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}