{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:22Z","timestamp":1753894402534,"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>The pebbling comonad, introduced by Abramsky, Dawar and Wang, provides a\ncategorical interpretation for the k-pebble games from finite model theory. The\ncoKleisli category of the pebbling comonad specifies equivalences under\ndifferent fragments and extensions of infinitary k-variable logic. Moreover,\nthe coalgebras over this pebbling comonad characterise treewidth and correspond\nto tree decompositions. In this paper we introduce the pebble-relation comonad,\nwhich characterises pathwidth and whose coalgebras correspond to path\ndecompositions. We further show that the existence of a coKleisli morphism in\nthis comonad is equivalent to truth preservation in the restricted conjunction\nfragment of k-variable infinitary logic. We do this using Dalmau's\npebble-relation game and an equivalent all-in-one pebble game. We then provide\na similar treatment to the corresponding coKleisli isomorphisms via a bijective\nversion of the all-in-one pebble game. Finally, we show as a consequence a new\nLov\\'asz-type theorem relating pathwidth to the restricted conjunction fragment\nof k-variable infinitary logic with counting quantifiers.<\/jats:p>","DOI":"10.46298\/lmcs-20(2:9)2024","type":"journal-article","created":{"date-parts":[[2024,5,17]],"date-time":"2024-05-17T10:15:15Z","timestamp":1715940915000},"source":"Crossref","is-referenced-by-count":0,"title":["The Pebble-Relation Comonad in Finite Model Theory"],"prefix":"10.46298","volume":"Volume 20, Issue 2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9814-7323","authenticated-orcid":false,"given":"Yo\u00e0v","family":"Montacute","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2844-0828","authenticated-orcid":false,"given":"Nihil","family":"Shah","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2024,5,17]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/13611\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/13611\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,17]],"date-time":"2024-05-17T10:15:16Z","timestamp":1715940916000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/10884"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,17]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(2:9)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2110.08196v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2110.08196v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2110.08196","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2110.08196","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2024,5,17]]},"article-number":"10884"}}