{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:35:33Z","timestamp":1753889733724,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2013,10,16]],"date-time":"2013-10-16T00:00:00Z","timestamp":1381881600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"crossref","award":["ANR-10-BLAN-0213"],"award-info":[{"award-number":["ANR-10-BLAN-0213"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Ludics is a reconstruction of logic with interaction as a primitive notion,\nin the sense that the primary logical concepts are no more formulas and proofs\nbut cut-elimination interpreted as an interaction between objects called\ndesigns. When the interaction between two designs goes well, such two designs\nare said to be orthogonal. A behaviour is a set of designs closed under\nbi-orthogonality. Logical formulas are then denoted by behaviours. Finally\nproofs are interpreted as designs satisfying particular properties. In that\nway, designs are more general than proofs and we may notice in particular that\nthey are not typed objects. Incarnation is introduced by Girard in Ludics as a\ncharacterization of \"useful\" designs in a behaviour. The incarnation of a\ndesign is defined as its subdesign that is the smallest one in the behaviour\nordered by inclusion. It is useful in particular because being \"incarnated\" is\none of the conditions for a design to denote a proof of a formula. The\ncomputation of incarnation is important also as it gives a minimal denotation\nfor a formula, and more generally for a behaviour. We give here a constructive\nway to capture the incarnation of the behaviour of a set of designs, without\ncomputing the behaviour itself. The method we follow uses an alternative\ndefinition of designs: rather than defining them as sets of chronicles, we\nconsider them as sets of paths, a concept very close to that of play in game\nsemantics that allows an easier handling of the interaction: the unfolding of\ninteraction is a path common to two interacting designs.<\/jats:p>","DOI":"10.2168\/lmcs-9(4:6)2013","type":"journal-article","created":{"date-parts":[[2014,7,15]],"date-time":"2014-07-15T09:37:51Z","timestamp":1405417071000},"source":"Crossref","is-referenced-by-count":0,"title":["Incarnation in Ludics and maximal cliques of paths"],"prefix":"10.46298","volume":"Volume 9, Issue 4","author":[{"given":"Myriam","family":"Quatrini","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christophe","family":"Fouquer\u00e9","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2013,10,16]]},"reference":[{"key":"598:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/926\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/926\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T19:59:11Z","timestamp":1681243151000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/926"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,16]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-9(4:6)2013","relation":{"is-same-as":[{"id-type":"arxiv","id":"1307.1028","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1307.1028","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2013,10,16]]},"article-number":"926"}}