{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T01:37:03Z","timestamp":1768354623685,"version":"3.49.0"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2018,10,31]],"date-time":"2018-10-31T00:00:00Z","timestamp":1540944000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2018,10,31]],"date-time":"2018-10-31T00:00:00Z","timestamp":1540944000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2018,10,31]],"date-time":"2018-10-31T00:00:00Z","timestamp":1540944000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called ILGL that gives an account of layering. The logic is a bunched system, combining the usual intuitionistic connectives, together with a non-commutative, non-associative conjunction (used to capture layering) and its associated implications. We give soundness and completeness theorems for a labelled tableaux system with respect to a Kripke semantics on graphs. We then give an equivalent relational semantics, itself proven equivalent to an algebraic semantics via a representation theorem. We utilise this result in two ways. First, we prove decidability of the logic by showing the finite embeddability property holds for the algebraic semantics. Second, we prove a Stone-type duality theorem for the logic. By introducing the notions of ILGL hyperdoctrine and indexed layered frame we are able to extend this result to a predicate version of the logic and prove soundness and completeness theorems for an extension of the layered graph semantics . We indicate the utility of predicate ILGL with a resource-labelled bigraph model.<\/jats:p>","DOI":"10.23638\/lmcs-14(4:11)2018","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:30:16Z","timestamp":1743701416000},"source":"Crossref","is-referenced-by-count":1,"title":["Intuitionistic Layered Graph Logic: Semantics and Proof Theory"],"prefix":"10.23638","volume":"Volume 14, Issue 4","author":[{"given":"Simon","family":"Docherty","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Pym","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2018,10,31]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1702.05795v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1702.05795v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:30:16Z","timestamp":1743701416000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/3163"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,31]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-14(4:11)2018","relation":{"has-preprint":[{"id-type":"arxiv","id":"1702.05795v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1702.05795v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1702.05795","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1702.05795","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,31]]},"article-number":"3163"}}