{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T16:08:53Z","timestamp":1762445333243},"reference-count":10,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2022,11,24]],"date-time":"2022-11-24T00:00:00Z","timestamp":1669248000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,1,25]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>There is a well-established correspondence between interpolation and amalgamation for algebraizable logics that satisfy certain additional assumptions. In this paper, we introduce the Robinson property of a logic and show that a conditionally algebraizable logic without any additional assumptions has the Robinson property if and only if the corresponding class of Lindenbaum\u2013Tarski algebras has the amalgamation property. Moreover, we give the logical characterization of the strong amalgamation property, solving an open problem of Andr\u00e9ka\u2013N\u00e9meti\u2013Sain. It is also shown that given the mentioned extra assumptions the Robinson property implies the interpolation property. As conditionally algebraizable logics cover algebraizable logics as well as various quantifier logics such as classical first order logic, our results yield a generalization of some of the results concerning interpolation and amalgamation.<\/jats:p>","DOI":"10.1093\/jigpal\/jzac076","type":"journal-article","created":{"date-parts":[[2022,11,25]],"date-time":"2022-11-25T12:23:06Z","timestamp":1669378986000},"page":"180-196","source":"Crossref","is-referenced-by-count":1,"title":["Amalgamation and Robinson property in universal algebraic logic"],"prefix":"10.1093","volume":"32","author":[{"given":"Zal\u00e1n","family":"Gyenis","sequence":"first","affiliation":[{"name":"Jagiellonian University , Krak\u00f3w"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00d6vge","family":"\u00d6zt\u00fcrk","sequence":"additional","affiliation":[{"name":"E\u00f6tv\u00f6s Lor\u00e1nd University , Budapest"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,11,24]]},"reference":[{"key":"2024012600290742900_ref1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-031-14887-3","article-title":"Universal Algebraic Logic","author":"Andr\u00e9ka","year":"2022"},{"key":"2024012600290742900_ref2","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/978-94-017-0452-6_3","article-title":"Algebraic logic","volume-title":"Handbook of Philosophical Logic","author":"Andr\u00e9ka","year":"2001"},{"key":"2024012600290742900_ref3","doi-asserted-by":"crossref","DOI":"10.1090\/memo\/0396","article-title":"Algebraizable logics","volume":"77","author":"Blok","year":"1989","journal-title":"Memoirs of the American Mathematical Society"},{"key":"2024012600290742900_ref4","article-title":"Abstract algebraic logic","volume-title":"Lecture Notes of the Summer School \u201cAlgebraic Logic and the Methodology of Applying It\u201d","author":"Blok","year":"1994"},{"key":"2024012600290742900_ref5","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/BF00403332","article-title":"Logical matrices and the amalgamation property","volume":"41","author":"Czelakowski","year":"1982","journal-title":"Studia Logica"},{"key":"2024012600290742900_ref6","article-title":"Amalgamation and interpolation in abstract algebraic logic","volume-title":"Models, Algebras, and Proofs, Selected Papers of the X Latin American Symposium on Mathematical Logic Held in Bogot\u00e1","author":"Czelakowski","year":"1999"},{"key":"2024012600290742900_ref7","article-title":"Abstract algebraic logic: an introductory textbook","volume-title":"Studies in Logic, Mathematical logic and Foundations","author":"Font","year":"2016"},{"key":"2024012600290742900_ref8","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/BF00370682","article-title":"Amalgamation and interpolation in normal modal logics","volume":"50","author":"Maksimova","year":"1991","journal-title":"Studia Logica"},{"key":"2024012600290742900_ref9","first-page":"556","article-title":"Interpolation theorems in modal logics and amalgamable varieties of topoboolean algebras","volume":"18","author":"Maksimova","year":"1979","journal-title":"Algebra i Logika"},{"key":"2024012600290742900_ref10","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/BF02944991","article-title":"Amalgamation, congruence extension and interpolation properties in algebras","volume":"1","author":"Pigozzi","year":"1972","journal-title":"Algebra Universalis"}],"container-title":["Logic Journal of the IGPL"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/32\/1\/180\/56419777\/jzac076.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/32\/1\/180\/56419777\/jzac076.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T00:29:19Z","timestamp":1706228959000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jigpal\/article\/32\/1\/180\/6840204"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,24]]},"references-count":10,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,11,24]]},"published-print":{"date-parts":[[2024,1,25]]}},"URL":"https:\/\/doi.org\/10.1093\/jigpal\/jzac076","relation":{},"ISSN":["1367-0751","1368-9894"],"issn-type":[{"value":"1367-0751","type":"print"},{"value":"1368-9894","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2024,2]]},"published":{"date-parts":[[2022,11,24]]}}}