The calculus of neo-Peircean relations

[2505.05306] The calculus of neo-Peircean relations Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Logic in Computer Science arXiv:2505.05306 (cs) [Submitted on 8 May 2025 ( v1 ), last revised 18 Jun 2026 (this version, v6)] Title: The calculus of neo-Peircean relations Authors: Filippo Bonchi , Alessandro Di Giorgio , Nathan Haydon , Pawel Sobocinski View a PDF of the paper titled The calculus of neo-Peircean relations, by Filippo Bonchi and 3 other authors View PDF Abstract: The calculus of relations was introduced by De Morgan and Peirce during the second half of the 19th century, as an extension of Boole's algebra of classes. Later developments on quantification theory by Frege and Peirce himself, paved the way to what is known today as first-order logic, causing the calculus of relations to be long forgotten. This was until 1941, when Tarski raised the question on the existence of a complete axiomatisation for it. This question found only negative answers: there is no finite axiomatisation for the calculus of relations and many of its fragments, as shown later by several no-go theorems. In this paper we show that -- by moving from traditional syntax (cartesian) to a diagrammatic one (monoidal) -- it is possible to have complete axiomatisations for the full calculus. The no-go theorems are circumvented by the fact that our calculus, named the calculus of neo-Peircean relations, is more expressive than the calculus of relations and, actually, as expressive as first-order logic. The axioms are obtained by combining two well known categorical structures: cartesian and linear bicategories. Comments: arXiv admin note: substantial text overlap with arXiv:2401.07055 Subjects: Logic in Computer Science (cs.LO) Cite as: arXiv:2505.05306 [cs.LO] (or arXiv:2505.05306v6 [cs.LO] for this version) https://doi.org/10.48550/arXiv.2505.05306 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Logical Methods in Computer Science, Volume 22, Issue 2 (June 19, 2026) lmcs:15645 Related DOI : https://doi.org/10.46298/lmcs-22%282%3A29%292026 Focus to learn more DOI(s) linking to related resources Submission history From: Alessandro Di Giorgio [ view email ] [via LMCS proxy] [v1] Thu, 8 May 2025 14:52:25 UTC (308 KB) [v2] Fri, 9 May 2025 12:18:43 UTC (308 KB) [v3] Fri, 31 Oct 2025 14:08:49 UTC (268 KB) [v4] Thu, 9 Apr 2026 06:42:59 UTC (317 KB) [v5] Tue, 16 Jun 2026 00:29:05 UTC (310 KB) [v6] Thu, 18 Jun 2026 13:48:11 UTC (310 KB) Full-text links: Access Paper: View a PDF of the paper titled The calculus of neo-Peircean relations, by Filippo Bonchi and 3 other authors View PDF TeX Source view license Current browse context: cs.LO < prev | next > new | recent | 2025-05 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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