{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T18:05:11Z","timestamp":1785261911737,"version":"3.55.0"},"reference-count":44,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2023,6,30]],"date-time":"2023-06-30T00:00:00Z","timestamp":1688083200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We generalize the notion of <jats:italic>consequence relation<\/jats:italic> standard in abstract treatments of logic to accommodate intuitions of <jats:italic>relevance<\/jats:italic>. The guiding idea follows the <jats:italic>use criterion<\/jats:italic>, according to which in order for some premises to have some conclusion(s) as consequence(s), the premises must each be <jats:italic>used<\/jats:italic> in some way to obtain the conclusion(s). This relevance intuition turns out to require not just a failure of monotonicity, but also a move to considering consequence relations as obtaining between <jats:italic>multisets<\/jats:italic>. We motivate and state basic definitions of relevant consequence relations, both in single conclusion (asymmetric) and multiple conclusion (symmetric) settings, as well as derivations and theories, guided by the use intuitions, and prove a number of results indicating that the definitions capture the desired results (at least in many cases).<\/jats:p>","DOI":"10.1017\/s1755020323000205","type":"journal-article","created":{"date-parts":[[2023,6,30]],"date-time":"2023-06-30T09:37:38Z","timestamp":1688117858000},"page":"762-792","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":3,"title":["RELEVANT CONSEQUENCE RELATIONS: AN INVITATION"],"prefix":"10.1017","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5597-6794","authenticated-orcid":false,"given":"GUILLERMO","family":"BADIA","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8570-9657","authenticated-orcid":false,"given":"LIBOR","family":"B\u011aHOUNEK","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3617-1392","authenticated-orcid":false,"given":"PETR","family":"CINTULA","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2303-003X","authenticated-orcid":false,"given":"ANDREW","family":"TEDDER","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2023,6,30]]},"reference":[{"key":"S1755020323000205_r28","doi-asserted-by":"publisher","DOI":"10.1080\/00048408212340551"},{"key":"S1755020323000205_r27","doi-asserted-by":"publisher","DOI":"10.1007\/BF00652071"},{"key":"S1755020323000205_r23","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/9055.001.0001"},{"key":"S1755020323000205_r13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-85675-5"},{"key":"S1755020323000205_r16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-71258-7_7"},{"key":"S1755020323000205_r17","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198531920.001.0001","volume-title":"Algebraic Methods in Philosophical Logic","author":"Dunn","year":"2001"},{"key":"S1755020323000205_r30","doi-asserted-by":"publisher","DOI":"10.2307\/j.ctv2x8v8c7.12"},{"key":"S1755020323000205_r35","volume-title":"An Algebraic Approach to Non-Classical Logics","author":"Rasiowa","year":"1974"},{"key":"S1755020323000205_r36","volume-title":"Relevant Logic: A Philosophical Examination of Inference","author":"Read","year":"1988"},{"key":"S1755020323000205_r41","doi-asserted-by":"publisher","DOI":"10.26686\/ajl.v19i1.7449"},{"key":"S1755020323000205_r24","volume-title":"Bridges from Classical to Non-Monotonic Logic","author":"Makinson","year":"2005"},{"key":"S1755020323000205_r25","doi-asserted-by":"publisher","DOI":"10.1145\/1071596.1071600"},{"key":"S1755020323000205_r20","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198538332.001.0001","volume-title":"Labelled Deductive Systems","author":"Gabbay","year":"1996"},{"key":"S1755020323000205_r39","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198537779.001.0001","volume-title":"Substructural Logics","author":"Schroeder-Heister","year":"1993"},{"key":"S1755020323000205_r4","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(91)90023-U"},{"key":"S1755020323000205_r33","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-3179-9"},{"key":"S1755020323000205_r40","first-page":"409","volume-title":"Logic, Semantics, Metamathematics: Papers from 1923 to 1938","author":"Tarski","year":"1956"},{"key":"S1755020323000205_r15","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-020-09560-x"},{"key":"S1755020323000205_r22","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1245158085"},{"key":"S1755020323000205_r31","first-page":"241","volume-title":"Paraconsistency: The Logical Way to the Inconsistent","author":"Meyer","year":"2002"},{"key":"S1755020323000205_r32","doi-asserted-by":"publisher","DOI":"10.12775\/LLP.2001.007"},{"key":"S1755020323000205_r34","doi-asserted-by":"publisher","DOI":"10.1007\/s11787-008-0034-2"},{"key":"S1755020323000205_r8","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-006-8299-z"},{"key":"S1755020323000205_r26","unstructured":"[26] Meyer, R. 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Published by Cambridge University Press on behalf of The Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}