{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:36:05Z","timestamp":1753889765887,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2008,8,6]],"date-time":"2008-08-06T00:00:00Z","timestamp":1217980800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Propositional canonical Gentzen-type systems, introduced in 2001 by Avron and\nLev, are systems which in addition to the standard axioms and structural rules\nhave only logical rules in which exactly one occurrence of a connective is\nintroduced and no other connective is mentioned. A constructive coherence\ncriterion for the non-triviality of such systems was defined and it was shown\nthat a system of this kind admits cut-elimination iff it is coherent. The\nsemantics of such systems is provided using two-valued non-deterministic\nmatrices (2Nmatrices). In 2005 Zamansky and Avron extended these results to\nsystems with unary quantifiers of a very restricted form. In this paper we\nsubstantially extend the characterization of canonical systems to (n,k)-ary\nquantifiers, which bind k distinct variables and connect n formulas, and show\nthat the coherence criterion remains constructive for such systems. Then we\nfocus on the case of k&amp;#8712;{0,1} and for a canonical calculus G show that it\nis coherent precisely when it has a strongly characteristic 2Nmatrix, which in\nturn is equivalent to admitting strong cut-elimination.<\/jats:p>","DOI":"10.2168\/lmcs-4(3:2)2008","type":"journal-article","created":{"date-parts":[[2009,1,9]],"date-time":"2009-01-09T10:20:38Z","timestamp":1231496438000},"source":"Crossref","is-referenced-by-count":6,"title":["Canonical calculi with (n,k)-ary quantifiers"],"prefix":"10.46298","volume":"Volume 4, Issue 3","author":[{"given":"Arnon","family":"Avron","sequence":"first","affiliation":[]},{"given":"Anna","family":"Zamansky","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2008,8,6]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1139\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1139\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:04:22Z","timestamp":1681243462000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1139"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,8,6]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2168\/lmcs-4(3:2)2008","relation":{"is-same-as":[{"id-type":"arxiv","id":"0806.0081","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.0806.0081","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2008,8,6]]},"article-number":"1139"}}