{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:25Z","timestamp":1753894405089,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Game comonads, introduced by Abramsky, Dawar and Wang and developed by\nAbramsky and Shah, give an interesting categorical semantics to some\nSpoiler-Duplicator games that are common in finite model theory. In particular\nthey expose connections between one-sided and two-sided games, and parameters\nsuch as treewidth and treedepth and corresponding notions of decomposition. In\nthe present paper, we expand the realm of game comonads to logics with\ngeneralised quantifiers. In particular, we introduce a comonad graded by two\nparameters $n \\leq k$ such that isomorphisms in the resulting Kleisli category\nare exactly Duplicator winning strategies in Hella's $n$-bijection game with\n$k$ pebbles. We define a one-sided version of this game which allows us to\nprovide a categorical semantics for a number of logics with generalised\nquantifiers. We also give a novel notion of tree decomposition that emerges\nfrom the construction.<\/jats:p>","DOI":"10.46298\/lmcs-20(3:8)2024","type":"journal-article","created":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T12:55:27Z","timestamp":1721739327000},"source":"Crossref","is-referenced-by-count":0,"title":["Game Comonads &amp; Generalised Quantifiers"],"prefix":"10.46298","volume":"Volume 20, Issue 3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3032-5514","authenticated-orcid":false,"given":"Adam \u00d3","family":"Conghaile","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4014-8248","authenticated-orcid":false,"given":"Anuj","family":"Dawar","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2024,7,23]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/13969\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/13969\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T07:15:14Z","timestamp":1721805314000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/7643"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,23]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(3:8)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2006.16039v4","asserted-by":"subject"},{"id-type":"arxiv","id":"2006.16039v3","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2006.16039","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2006.16039","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2024,7,23]]},"article-number":"7643"}}