{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T12:04:30Z","timestamp":1753877070836,"version":"3.41.2"},"reference-count":20,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2024,8,28]],"date-time":"2024-08-28T00:00:00Z","timestamp":1724803200000},"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":[[2025,5,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In recent research, some of the present authors introduced the concept of an $n$-dimensional Boolean algebra and its corresponding propositional logic $n\\textrm{CL}$, generalizing the Boolean propositional calculus to $n\\geq 2$ perfectly symmetric truth values. This paper presents a sound and complete sequent calculus for $n\\textrm{CL}$, named $n\\textrm{LK}$. We provide two proofs of completeness: one syntactic and one semantic. The former implies as a corollary that $n\\textrm{LK}$ enjoys the cut admissibility property. The latter relies on the generalization to the $n$-ary case of the classical proof based on the Lindenbaum algebra of formulas and Boolean ultrafilters.<\/jats:p>","DOI":"10.1093\/jigpal\/jzae100","type":"journal-article","created":{"date-parts":[[2024,8,28]],"date-time":"2024-08-28T14:19:20Z","timestamp":1724854760000},"source":"Crossref","is-referenced-by-count":0,"title":["The higher dimensional propositional calculus"],"prefix":"10.1093","volume":"33","author":[{"given":"A","family":"Bucciarelli","sequence":"first","affiliation":[{"name":"IRIF, CNRS and Universit\u00e9 Paris Cit\u00e9, Paris , , buccia@irif.fr","place":["France"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P-L","family":"Curien","sequence":"additional","affiliation":[{"name":"IRIF, CNRS and Universit\u00e9 Paris Cit\u00e9, Paris , , curien@irif.fr","place":["France"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A","family":"Ledda","sequence":"additional","affiliation":[{"name":"Dipartimento di Pedagogia, Psicologia, Filosofia, Universit\u00e0 di Cagliari , Cagliari, , antonio.ledda@unica.it","place":["Italy"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F","family":"Paoli","sequence":"additional","affiliation":[{"name":"Dipartimento di Pedagogia, Psicologia, Filosofia, Universit\u00e0 di Cagliari , Cagliari, , paoli@unica.it","place":["Italy"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A","family":"Salibra","sequence":"additional","affiliation":[{"name":"IRIF, CNRS and Universit\u00e9 Paris Cit\u00e9, Paris , , salibra@irif.fr","place":["France"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,8,28]]},"reference":[{"key":"2025052605515676400_ref1","doi-asserted-by":"crossref","first-page":"939","DOI":"10.2307\/2273828","article-title":"A constructive analysis of RM","volume":"52","author":"Avron","year":"1987","journal-title":"Journal of Symbolic Logic"},{"key":"2025052605515676400_ref2","first-page":"36","article-title":"Analytic calculi for projective logics","volume-title":"Tableaux \u201999","author":"Baaz","year":"1999"},{"key":"2025052605515676400_ref3","first-page":"192","article-title":"Dual systems of sequents and tableaux for many-valued logics","volume":"51","author":"Baaz","year":"1993","journal-title":"Bulletin of the European Association for Theoretical Computer Science"},{"key":"2025052605515676400_ref4","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/978-3-031-44490-6_13","article-title":"Boolean-like algebras of finite dimension: from Boolean products to semiring product","volume-title":"Janusz Czelakowski on Logical Consequence, Outstanding Contributions to Logic","author":"Bucciarelli","year":"2024"},{"key":"2025052605515676400_ref5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.26493\/2590-9770.1323.ceb","article-title":"On noncommutative generalisations of Boolean algebras","volume":"2","author":"Bucciarelli","year":"2019","journal-title":"The Art of Discrete and Applied Mathematics"},{"key":"2025052605515676400_ref6","article-title":"A course in universal algebra","volume-title":"Graduate Texts in Mathematics","author":"Burris","year":"1981"},{"key":"2025052605515676400_ref7","first-page":"496","article-title":"Uniform rules and dialogue games for fuzzy logics","volume-title":"LPAR 2004, LNCS","author":"Ciabattoni","year":"2004"},{"key":"2025052605515676400_ref8","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.tcs.2013.02.003","article-title":"Proof theory for locally finite many-valued logics: Semi-projective logics","volume":"480","author":"Ciabattoni","year":"2013","journal-title":"Theoretical Computer Science"},{"key":"2025052605515676400_ref9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3390\/axioms8040118","article-title":"Hybrid deduction-refutation systems","volume":"8","author":"Goranko","year":"2019","journal-title":"Axioms"},{"key":"2025052605515676400_ref10","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/978-981-15-2221-5_9","article-title":"Refutation systems: An overview and some applications to philosophical logics","volume-title":"Knowledge, Proof and Dynamics, Outstanding Contributions to Logic","author":"Goranko","year":"2020"},{"key":"2025052605515676400_ref11","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1093\/logcom\/exn067","article-title":"Combining derivations and refutations for cut-free completeness in bi-intuitionistic logic","volume":"20","author":"Gore","year":"2010","journal-title":"Journal of Logic and Computation"},{"key":"2025052605515676400_ref12","first-page":"101","article-title":"On semi-boolean-like algebras","volume":"52","author":"Ledda","year":"2013","journal-title":"Acta Universitatis Palackianae Olomucensis. 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