{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T15:40:27Z","timestamp":1774453227644,"version":"3.50.1"},"reference-count":7,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T00:00:00Z","timestamp":1687219200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,7,24]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Subresiduated lattices were introduced during the decade of 1970 by Epstein and Horn as an algebraic counterpart of some logics with strong implication previously studied by Lewy and Hacking. These logics are examples of subintuitionistic logics, i.e. logics in the language of intuitionistic logic that are defined semantically by using Kripke models, in the same way as intuitionistic logic is defined, but without requiring of the models some of the properties required in the intuitionistic case. Also in relation with the study of subintuitionistic logics, Celani and Jansana get these algebras as the elements of a subvariety of that of weak Heyting algebras. Here, we study both the implicative and the implicative-infimum subreducts of subresiduated lattices. Besides, we propose a calculus whose equivalent algebraic semantics is given by these classes of algebras. Several expansions of these calculi are also studied together with some interesting properties of them.<\/jats:p>","DOI":"10.1093\/logcom\/exad042","type":"journal-article","created":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T08:36:11Z","timestamp":1721723771000},"page":"856-886","source":"Crossref","is-referenced-by-count":6,"title":["On subreducts of subresiduated lattices and some related logics"],"prefix":"10.1093","volume":"34","author":[{"given":"Jos\u00c9 Luis","family":"Castiglioni","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ciencias Exactas (UNLP) , Casilla de correos 172, La Plata 1900, Argentina, CONICET, Argentina"}],"role":[{"role":"author","vocab":"crossref"}]},{"given":"V\u00edctor","family":"Fern\u00c1ndez","sequence":"additional","affiliation":[{"name":"Universidad Nacional de San Juan , Avenida Jos\u00e9 I. de la Roza (Oeste) 230, San Juan 5400, Argentina"}],"role":[{"role":"author","vocab":"crossref"}]},{"given":"H\u00e9ctor Federico","family":"Mallea","sequence":"additional","affiliation":[{"name":"Universidad Nacional de San Juan, Avenida Jos\u00e9 I. de la Roza (Oeste) 230 , San Juan 5400, Argentina, CONICET, Argentina"}],"role":[{"role":"author","vocab":"crossref"}]},{"given":"Hern\u00c1n Javier","family":"San Mart\u00cdn","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ciencias Exactas (UNLP) , Casilla de correos 172, La Plata 1900, Argentina, CONICET, Argentina"}],"role":[{"role":"author","vocab":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2023,6,20]]},"reference":[{"key":"2024072308354770300_ref1","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s00153-021-00777-4","article-title":"On Hilbert algebras generated by the order","volume":"61","author":"Castiglioni","year":"2022","journal-title":"Archive for Mathematical Logic"},{"key":"2024072308354770300_ref2","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1007\/s11225-022-10020-7","article-title":"Sub-Hilbert lattices","volume":"111","author":"Castiglioni","year":"2023","journal-title":"Studia Logica"},{"key":"2024072308354770300_ref3","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1002\/malq.200410022","article-title":"Bounded distributive lattices with strict implication","volume":"51","author":"Celani","year":"2005","journal-title":"Mathematical Logic Quarterly"},{"key":"2024072308354770300_ref4","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1305\/ndjfl\/1063372244","article-title":"A closer look at some subintuitionistic logics","volume":"42","author":"Celani","year":"2001","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"2024072308354770300_ref5","article-title":"Notas de L\u00f3gica Matem\u00e1tica","volume-title":"Sobre Algebras de Hilbert","author":"Diego","year":"1965"},{"key":"2024072308354770300_ref6","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1002\/malq.19760220128","article-title":"Logics which are characterized by subresiduated lattices","volume":"22","author":"Epstein","year":"1976","journal-title":"Z. Math. Logik Grundlagen Math."},{"key":"2024072308354770300_ref7","article-title":"Studies in Logic 60","volume-title":"Abstract Algebraic Logic. An Introductory Textbook","author":"Font","year":"2016"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/34\/5\/856\/58611842\/exad042.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/34\/5\/856\/58611842\/exad042.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T08:36:17Z","timestamp":1721723777000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/34\/5\/856\/7203658"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,20]]},"references-count":7,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,6,20]]},"published-print":{"date-parts":[[2024,7,24]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exad042","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"value":"0955-792X","type":"print"},{"value":"1465-363X","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2024,7]]},"published":{"date-parts":[[2023,6,20]]}}}