eprintid: 10198560 rev_number: 9 eprint_status: archive userid: 699 dir: disk0/10/19/85/60 datestamp: 2024-10-16 08:32:27 lastmod: 2024-10-16 08:32:27 status_changed: 2024-10-16 08:32:27 type: proceedings_section metadata_visibility: show sword_depositor: 699 creators_name: Bonchi, Filippo creators_name: Di Giorgio, Alessandro creators_name: Trotta, Davide title: When Lawvere Meets Peirce: An Equational Presentation of Boolean Hyperdoctrines ispublished: pub divisions: UCL divisions: B04 divisions: F48 keywords: Relational algebra; hyperdoctrines; cartesian bicategories; string diagrams note: Copyright © Filippo Bonchi, Alessandro Di Giorgio, and Davide Trotta; licensed under Creative Commons License CC-BY 4.0, https://creativecommons.org/licenses/by/4.0/legalcode. abstract: Fo-bicategories are a categorification of Peirce’s calculus of relations. Notably, their laws provide a proof system for first-order logic that is both purely equational and complete. This paper illustrates a correspondence between fo-bicategories and Lawvere’s hyperdoctrines. To streamline our proof, we introduce peircean bicategories, which offer a more succinct characterization of fo-bicategories. date: 2024-08-23 date_type: published publisher: Dagstuhl Publishing official_url: https://doi.org/10.4230/LIPIcs.MFCS.2024.30 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 2319487 doi: 10.4230/LIPIcs.MFCS.2024.30 lyricists_name: Di Giorgio, Alessandro lyricists_id: ADIGI07 actors_name: Di Giorgio, Alessandro actors_id: ADIGI07 actors_role: owner full_text_status: public pres_type: paper series: Leibniz International Proceedings in Informatics (LIPIcs) publication: Leibniz International Proceedings in Informatics, LIPIcs volume: 306 place_of_pub: Wadern, Germany pagerange: 30:1-30:19 event_title: Mathematical Foundations of Computer Science (MFCS) issn: 1868-8969 book_title: 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024) editors_name: Královič, Rastislav editors_name: Kučera, Antonín citation: Bonchi, Filippo; Di Giorgio, Alessandro; Trotta, Davide; (2024) When Lawvere Meets Peirce: An Equational Presentation of Boolean Hyperdoctrines. In: Královič, Rastislav and Kučera, Antonín, (eds.) 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). (pp. 30:1-30:19). Dagstuhl Publishing: Wadern, Germany. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10198560/1/LIPIcs.MFCS.2024.30.pdf