{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T10:19:33Z","timestamp":1772533173308,"version":"3.50.1"},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2015,2,3]],"date-time":"2015-02-03T00:00:00Z","timestamp":1422921600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2015,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper explores how a semantics for Prior\u2019s infamous connective tonk should be, a connective defined by inference rules that trivialize the logic of a deductive system if that logic is supposed to be transitive. To avoid triviality, one must reject transitivity and in a relatively recent paper, Roy Cook develops a semantics for tonk with non-transitive entailment. However, I show in this paper that a cut-free sequent calculus for tonk - the arguably most natural and simplest deductive system for a non-transitive logic - can neither be complete with respect to Cook\u2019s semantics nor with respect to a semantics with non-transitive entailment based on a semantics for vagueness and transparent truth developed by Cobreros <jats:italic>et al.<\/jats:italic> It is argued that the failure to adequately represent tonk is connected with the fact that tonk is not uniquely defined in a cut-free sequent calculus system unless the logic is in addition non-reflexive. To remedy this, the paper develops a semantics with non-transitive and non-reflexive entailment based on the idea that complex formulae are true or false relative to them being assessed as premise or as conclusion.<\/jats:p>","DOI":"10.1017\/s1755020314000513","type":"journal-article","created":{"date-parts":[[2015,2,3]],"date-time":"2015-02-03T06:48:03Z","timestamp":1422946083000},"page":"488-505","source":"Crossref","is-referenced-by-count":15,"title":["HOW A SEMANTICS FOR TONK SHOULD BE"],"prefix":"10.1017","volume":"8","author":[{"given":"ANDREAS","family":"FJELLSTAD","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2015,2,3]]},"reference":[{"key":"S1755020314000513_ref12","doi-asserted-by":"publisher","DOI":"10.1093\/analys\/21.2.38"},{"key":"S1755020314000513_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801174"},{"key":"S1755020314000513_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-010-9165-z"},{"key":"S1755020314000513_ref1","doi-asserted-by":"publisher","DOI":"10.1093\/analys\/22.6.130"},{"key":"S1755020314000513_ref3","doi-asserted-by":"publisher","DOI":"10.1093\/mind\/fzt110"},{"key":"S1755020314000513_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-004-7805-x"},{"key":"S1755020314000513_ref5","volume-title":"The Logical Basis of Metaphysics","author":"Dummett","year":"1991"},{"key":"S1755020314000513_ref6","volume-title":"The Stanford Encyclopedia of Philosophy","author":"Gupta","year":"2009"},{"key":"S1755020314000513_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-010-9153-3"},{"key":"S1755020314000513_ref7","unstructured":"Hjortland O. T . (2009). The structure of logical consequence: Proof-theoretic conceptions. PhD thesis, University of St. Andrews."},{"key":"S1755020314000513_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511527340"},{"key":"S1755020314000513_ref9","volume-title":"The Routledge Companion to the Philosophy of Language","author":"MacFarlane","year":"2012"},{"key":"S1755020314000513_ref14","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020312000056"},{"key":"S1755020314000513_ref15","doi-asserted-by":"publisher","DOI":"10.1080\/00048402.2011.630010"},{"key":"S1755020314000513_ref16","article-title":"Anything goes","author":"Ripley","year":"2014","journal-title":"Topoi"},{"key":"S1755020314000513_ref17","first-page":"27","volume-title":"Selected Papers Contributed to the Sections of GAP.5, Fifth International Congress of the Society for Analytic Philosophy, Bielefeld, September 2003","author":"Schroeder-Heister","year":"2004"},{"key":"S1755020314000513_ref19","doi-asserted-by":"publisher","DOI":"10.1093\/analys\/21.6.124"},{"key":"S1755020314000513_ref20","doi-asserted-by":"publisher","DOI":"10.2307\/2102968"},{"key":"S1755020314000513_ref21","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139168717"},{"key":"S1755020314000513_ref13","volume-title":"Methodology and Philosophy of Science: Proceedings of the Twelfth International Congress","author":"Restall","year":"2005"},{"key":"S1755020314000513_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/BF00183072"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020314000513","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,20]],"date-time":"2019-04-20T19:58:19Z","timestamp":1555790299000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020314000513\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,3]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,9]]}},"alternative-id":["S1755020314000513"],"URL":"https:\/\/doi.org\/10.1017\/s1755020314000513","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,3]]}}}