{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:13:02Z","timestamp":1759637582815},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":376,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2013,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The implicational fragment of the logic of relevant implication, <jats:italic>R<\/jats:italic><jats:sub>\u2192<\/jats:sub> is known to be decidable. We show that the implicational fragment of the logic of ticket entailment, <jats:italic>T<\/jats:italic><jats:sub>\u2192<\/jats:sub> is <jats:italic>decidable<\/jats:italic>. Our proof is based on the <jats:italic>consecution calculus<\/jats:italic> that we introduced specifically to solve this 50-year old open problem. We reduce the decidability problem of <jats:italic>T<\/jats:italic><jats:sub>\u2192<\/jats:sub> to the decidability problem of <jats:italic>R<\/jats:italic><jats:sub>\u2192<\/jats:sub>. The decidability of <jats:italic>T<\/jats:italic><jats:sub>\u2192<\/jats:sub> is equivalent to the <jats:italic>decidability<\/jats:italic> of the <jats:italic>inhabitation<\/jats:italic> problem of implicational types by <jats:italic>combinators<\/jats:italic> over the base {B, B\u2032, I, W}.<\/jats:p>","DOI":"10.2178\/jsl.7801150","type":"journal-article","created":{"date-parts":[[2013,1,23]],"date-time":"2013-01-23T14:38:23Z","timestamp":1358951903000},"page":"214-236","source":"Crossref","is-referenced-by-count":16,"title":["On the decidability of implicational ticket entailment"],"prefix":"10.1017","volume":"78","author":[{"given":"Katalin","family":"Bimb\u00f3","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. 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