{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T01:12:58Z","timestamp":1685149978999},"reference-count":35,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T00:00:00Z","timestamp":1651449600000},"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":[[2023,5,25]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper focuses on order-preserving logics defined from varieties of distributive lattices with negation, and in particular on the problem of whether these can be axiomatized by means Hilbert-style calculi that are finite (i.e. that contain a finite number of finitary rule schemata). On the negative side, we provide a syntactic condition on the equational presentation of a variety that entails failure of finite axiomatizability for the corresponding logic. An application of this result is that the logic of all distributive lattices with negation is not finitely axiomatizable; we likewise establish that the order-preserving logic of the variety of all Ockham algebras is also not finitely axiomatizable. On the positive side, we show that an arbitrary subvariety of semi-De Morgan algebras is axiomatized by a finite number of equations if and only if the corresponding order-preserving logic is axiomatized by a finite Hilbert-style calculus. This equivalence also holds for every subvariety of a Berman variety of Ockham algebras. We obtain, as a corollary, a new proof that the implication-free fragment of intuitionistic logic is finitely axiomatizable, as well as a new corresponding Hilbert-style calculus. Our proofs are constructive in that they allow us to effectively convert an equational presentation of a variety of algebras into a Hilbert-style calculus for the corresponding order-preserving logic, and vice versa. We also consider the assertional logics associated to the above-mentioned varieties, showing in particular that the assertional logics of finitely axiomatizable subvarieties of semi-De Morgan algebras are finitely axiomatizable as well.<\/jats:p>","DOI":"10.1093\/jigpal\/jzac043","type":"journal-article","created":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T12:13:57Z","timestamp":1646914437000},"page":"510-533","source":"Crossref","is-referenced-by-count":0,"title":["Finite axiomatizability of logics of distributive lattices with negation"],"prefix":"10.1093","volume":"31","author":[{"given":"S\u00e9rgio","family":"Marcelino","sequence":"first","affiliation":[{"name":"SQIG\u2013Instituto de Telecomunica\u00e7\u00f5es, Departamento de Matem\u00e1tica , Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Umberto","family":"Rivieccio","sequence":"additional","affiliation":[{"name":"Departamento de Inform\u00e1tica e Matem\u00e1tica Aplicada, Universidade Federal do Rio Grande do Norte , 59072-970 Natal (RN), Brasil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,5,2]]},"reference":[{"key":"2023052700430791900_ref1","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1007\/s11225-017-9739-7","article-title":"An algebraic view of super-Belnap logics","volume":"105","author":"Albuquerque","year":"2017","journal-title":"Studia Logica"},{"key":"2023052700430791900_ref2","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1093\/logcom\/exi001","article-title":"Non-deterministic multiple-valued structures","volume":"15","author":"Avron","year":"2005","journal-title":"Journal of Logic and Computation"},{"key":"2023052700430791900_ref3","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s10817-013-9273-x","article-title":"Finite-valued semantics for canonical labelled calculi","volume":"51","author":"Baaz","year":"2013","journal-title":"Journal of Automated Reasoning"},{"key":"2023052700430791900_ref4","first-page":"30","article-title":"How a computer should think","volume-title":"Contemporary Aspects of Philosophy","author":"Belnap","year":"1976"},{"key":"2023052700430791900_ref5","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-010-1161-7_2","article-title":"A useful four-valued logic","volume-title":"Modern Uses of Multiple-Valued Logic","author":"Belnap","year":"1977"},{"key":"2023052700430791900_ref6","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/BF01836429","article-title":"Distributive lattices with an additional unary operation","volume":"16","author":"Berman","year":"1977","journal-title":"Aequationes Mathematicae"},{"key":"2023052700430791900_ref7","article-title":"Mem. 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