{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T20:40:49Z","timestamp":1770237649951,"version":"3.49.0"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T00:00:00Z","timestamp":1700179200000},"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":[[2025,2,27]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we introduce the variety of $I$-modal ririgs. We characterize the congruence lattice of its members by means of $I$-filters, and we provide a description of $I$-filter generation. We also provide an axiomatic presentation for the variety generated by chains of the subvariety of contractive $I$-modal ririgs. Finally, we introduce a Hilbert-style calculus for a logic with $I$-modal ririgs as an equivalent algebraic semantics and we prove that such a logic has the parametrized local deduction-detachment theorem.<\/jats:p>","DOI":"10.1093\/jigpal\/jzad025","type":"journal-article","created":{"date-parts":[[2023,11,18]],"date-time":"2023-11-18T00:15:18Z","timestamp":1700266518000},"page":"74-94","source":"Crossref","is-referenced-by-count":1,"title":["Modal expansions of ririgs"],"prefix":"10.1093","volume":"33","author":[{"given":"Agust\u00cdn L","family":"Nagy","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica , Facultad de Ciencias Exactas (UNCPBA), Pinto 399, Tandil, , agustin.nagy@gmail.com","place":["Argentina"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"William J","family":"Zuluaga Botero","sequence":"additional","affiliation":[{"name":"CONICET , Godoy Cruz 2290 (C1425FQB) CABA, , wizubo@gmail.com","place":["Argentina"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2023,11,17]]},"reference":[{"key":"2025012810511829000_ref1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107050884","article-title":"Cambridge Tracts in Theoretical Computer Science","volume-title":"Modal Logic","author":"Blackburn","year":"2001"},{"key":"2025012810511829000_ref2","article-title":"Memoirs of the American Mathematical Society A.M.S.","volume-title":"Algebraizable Logics","author":"Blok","year":"1989"},{"key":"2025012810511829000_ref3","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-8130-3","volume-title":"A Course in Universal Algebra","author":"Burris","year":"1981"},{"key":"2025012810511829000_ref4","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s11225-005-5170-6","article-title":"Implicit connectives of algebraizable logics","volume":"78","author":"Caicedo","year":"2004","journal-title":"Studia Logica"},{"key":"2025012810511829000_ref5","doi-asserted-by":"crossref","first-page":"1620","DOI":"10.2307\/2694965","article-title":"An algebraic approach to intuitionistic connectives","volume":"66","author":"Caicedo","year":"2001","journal-title":"Journal of Symbolic Logic"},{"key":"2025012810511829000_ref6","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s00012-016-0384-1","article-title":"Semantical conditions for the definability of functions and relations","volume":"76","author":"Campercholi","year":"2016","journal-title":"Algebra Universalis"},{"key":"2025012810511829000_ref7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/IJMMS\/2006\/21835","article-title":"Simple and subdirectly irreducibles bounded distributive lattices with unary operators","volume":"2006","author":"Celani","year":"2006","journal-title":"International Journal of Mathematics and Mathematical Sciences"},{"key":"2025012810511829000_ref8","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.fss.2022.05.019","article-title":"The variety of modal weak G\u00f6del algebras","volume":"456","author":"Celani","year":"2023","journal-title":"Fuzzy Sets and Systems"},{"key":"2025012810511829000_ref9","volume-title":"Semilattice Structures","author":"Chajda","year":"2007"},{"key":"2025012810511829000_ref10","doi-asserted-by":"crossref","first-page":"166","DOI":"10.2307\/2273953","article-title":"Intuitionistic tense and modal logic","volume":"51","author":"Ewald","year":"1986","journal-title":"Journal of Symbolic Logic"},{"key":"2025012810511829000_ref11","article-title":"Abstract algebraic logic\u2014an introductory textbook","volume-title":"Studies in Logic","author":"Font","year":"2016"},{"key":"2025012810511829000_ref12","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1007\/978-3-030-88701-8_11","article-title":"Some modal and temporal translations of generalized basic logic","volume-title":"Relational and Algebraic Methods in Computer Science","author":"Fussner","year":"2021"},{"key":"2025012810511829000_ref13","volume-title":"Residuated Lattices: An Algebraic Glimpse at Substructural Logics","author":"Galatos","year":"2007"},{"key":"2025012810511829000_ref14","volume-title":"Semirings and Affine Equations Over Them: Theory and Applications","author":"Golan","year":"2013"},{"key":"2025012810511829000_ref15","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1142\/S0218196702001048","article-title":"The structure of commutative residuated lattices","volume":"12","author":"Hart","year":"2002","journal-title":"International Journal of Algebra and Computation"},{"key":"2025012810511829000_ref16","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1002\/1521-3870(200105)47:2<187::AID-MALQ187>3.0.CO;2-J","article-title":"Heyting algebras with operators","volume":"47","author":"Hasimoto","year":"2001","journal-title":"Mathematical Logic Quarterly"},{"key":"2025012810511829000_ref17","volume-title":"Symbolic Logic","author":"Lewis","year":"1959"},{"key":"2025012810511829000_ref18","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.jalgebra.2013.11.019","article-title":"Amalgamation and interpolation in ordered algebras","volume":"402","author":"Metcalfe","year":"2014","journal-title":"Journal of Algebra"},{"key":"2025012810511829000_ref19","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511569852","article-title":"Cambridge Tracts in Theoretical Computer Science","volume-title":"Epistemic Logic for AI and Computer Science","author":"Meyer","year":"1995"},{"key":"2025012810511829000_ref20","volume-title":"Time and Modality","author":"Prior","year":"1957"},{"key":"2025012810511829000_ref21","first-page":"379","article-title":"Negative sets have Euler characteristic and dimension","volume-title":"Proceedings of Category Theory, Como, Italy, 1990","author":"Schanuel","year":"1991"},{"key":"2025012810511829000_ref22","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1023\/B:STUD.0000032087.02579.e2","article-title":"Rule separation and embedding theorems for logics without weakening","volume":"76","author":"Van Alten","year":"2004","journal-title":"Studia Logica"},{"key":"2025012810511829000_ref23","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/978-94-017-2109-7_17","article-title":"Intuitionistic modal logic","volume-title":"Logic and Foundations of Mathematics","author":"Wolter","year":"1999"}],"container-title":["Logic Journal of the IGPL"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/33\/1\/74\/53478568\/jzad025.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/33\/1\/74\/53478568\/jzad025.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T10:51:42Z","timestamp":1738061502000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jigpal\/article\/33\/1\/74\/7416508"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,17]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,2,27]]}},"URL":"https:\/\/doi.org\/10.1093\/jigpal\/jzad025","relation":{},"ISSN":["1367-0751","1368-9894"],"issn-type":[{"value":"1367-0751","type":"print"},{"value":"1368-9894","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025,2]]},"published":{"date-parts":[[2023,11,17]]}}}