{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T22:29:54Z","timestamp":1789165794856,"version":"build-2803163510"},"reference-count":39,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2019,2,15]],"date-time":"2019-02-15T00:00:00Z","timestamp":1550188800000},"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":[[2019,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We generalise the Blok\u2013J\u00f3nsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and J\u00f3nsson admit, in place of sheer formulas, a wider range of syntactic units to be manipulated in deductions (including sequents or equations), these objects are invariably<jats:italic>aggregated<\/jats:italic>via set-theoretical union. Our approach is more general in that nonidempotent forms of premiss and conclusion aggregation, including multiset sum and fuzzy set union, are considered. In their abstract form, thus,<jats:italic>deductive relations<\/jats:italic>are defined as additional compatible preorderings over certain partially ordered monoids. We investigate these relations using categorical methods and provide analogues of the main results obtained in the general theory of consequence relations. Then we focus on the driving example of multiset deductive relations, providing variations of the methods of matrix semantics and Hilbert systems in Abstract Algebraic Logic.<\/jats:p>","DOI":"10.1017\/s175502031900008x","type":"journal-article","created":{"date-parts":[[2019,2,15]],"date-time":"2019-02-15T10:15:01Z","timestamp":1550225701000},"page":"331-371","source":"Crossref","is-referenced-by-count":6,"title":["AN ABSTRACT APPROACH TO CONSEQUENCE RELATIONS"],"prefix":"10.1017","volume":"12","author":[{"given":"PETR","family":"CINTULA","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"JOS\u00c9","family":"GIL-F\u00c9REZ","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"TOMMASO","family":"MORASCHINI","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"FRANCESCO","family":"PAOLI","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2019,2,15]]},"reference":[{"key":"S175502031900008X_ref39","volume-title":"Lectures on Linear Logic","volume":"29","author":"Troelstra","year":"1992"},{"key":"S175502031900008X_ref37","first-page":"33","article-title":"A systematization of fundamentals of multisets","volume":"29","author":"Singh","year":"2008","journal-title":"Lecturas Matematicas"},{"key":"S175502031900008X_ref36","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2012.09.006"},{"key":"S175502031900008X_ref34","volume-title":"Mathematics Preprint Series","volume":"175","author":"Rebagliato","year":"1995"},{"key":"S175502031900008X_ref33","doi-asserted-by":"crossref","first-page":"319","DOI":"10.3233\/FI-1993-182-417","article-title":"On the algebraization of some Gentzen systems","volume":"18","author":"Rebagliato","year":"1993","journal-title":"Fundamenta Informaticae"},{"key":"S175502031900008X_ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2012.10.013"},{"key":"S175502031900008X_ref26","doi-asserted-by":"publisher","DOI":"10.1080\/00048408212340551"},{"key":"S175502031900008X_ref24","doi-asserted-by":"publisher","DOI":"10.1142\/3903"},{"key":"S175502031900008X_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-010-0201-z"},{"key":"S175502031900008X_ref20","volume-title":"Residuated Lattices: An Algebraic Glimpse at Substructural Logics","volume":"151","author":"Galatos","year":"2007"},{"key":"S175502031900008X_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-013-9536-x"},{"key":"S175502031900008X_ref17","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024621922509"},{"key":"S175502031900008X_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21591-3"},{"key":"S175502031900008X_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-2807-2"},{"key":"S175502031900008X_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-016-1209-7"},{"key":"S175502031900008X_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9480-6"},{"key":"S175502031900008X_ref10","doi-asserted-by":"publisher","DOI":"10.1090\/memo\/0396"},{"key":"S175502031900008X_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370269"},{"key":"S175502031900008X_ref6","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093634995"},{"key":"S175502031900008X_ref5","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1093\/oso\/9780198538592.003.0008","volume-title":"What is a logical system? 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