{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T20:10:52Z","timestamp":1757621452142,"version":"3.44.0"},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T00:00:00Z","timestamp":1738713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"name":"Shandong Provincial Natural Science Foundation, China","award":["ZR2023QF021"],"award-info":[{"award-number":["ZR2023QF021"]}]},{"name":"Taishan Young Scholars Program of the Government of Shandong Province, China","award":["tsqn201909151"],"award-info":[{"award-number":["tsqn201909151"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,7,29]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The symmetric strict implication calculus $\\mathsf{S}^{2}\\mathsf{IC}$ is a modal calculus for compact Hausdorff spaces. This is established through de Vries duality, linking compact Hausdorff spaces with de Vries algebras\u2014complete Boolean algebras equipped with a special relation. Modal compact Hausdorff spaces are compact Hausdorff spaces enriched with a continuous relation. These spaces correspond, via modalized de Vries duality, to upper continuous modal de Vries algebras. In this paper, we introduce the modal symmetric strict implication calculus $\\mathsf{MS}^{2}\\mathsf{IC}$, which extends $\\mathsf{S}^{2}\\mathsf{IC}$. We prove that $\\mathsf{MS}^{2}\\mathsf{IC}$ is strongly sound and complete with respect to upper continuous modal de Vries algebras, thereby providing a logical calculus for modal compact Hausdorff spaces. We also develop a relational semantics for $\\mathsf{MS}^{2}\\mathsf{IC}$ that we employ to show admissibility of various $\\Pi_{2}$-rules in this system.<\/jats:p>","DOI":"10.1093\/logcom\/exae086","type":"journal-article","created":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T01:29:06Z","timestamp":1738718946000},"source":"Crossref","is-referenced-by-count":0,"title":["A calculus for modal compact Hausdorff spaces"],"prefix":"10.1093","volume":"35","author":[{"given":"Nick","family":"Bezhanishvili","sequence":"first","affiliation":[{"name":"Institute for Logic , Language and Computation, University of Amsterdam, 1098 XH Amsterdam, the","place":["Netherlands"]}]},{"given":"Luca","family":"Carai","sequence":"additional","affiliation":[{"name":"Department of Mathematics , University of Milan, 20122 Milan,","place":["Italy"]}]},{"given":"Silvio","family":"Ghilardi","sequence":"additional","affiliation":[{"name":"Department of Mathematics , University of Milan, 20122 Milan,","place":["Italy"]}]},{"given":"Zhiguang","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics , Taishan University, Tai'an 271000,","place":["China"]}]}],"member":"286","published-online":{"date-parts":[[2025,2,5]]},"reference":[{"key":"2025090809271429400_ref1","first-page":"29","article-title":"Modal logics for region-based theories of space","volume":"81","author":"Balbiani","year":"2007","journal-title":"Fundamenta Informaticae"},{"key":"2025090809271429400_ref2","doi-asserted-by":"crossref","first-page":"1064","DOI":"10.1016\/j.topol.2010.01.007","article-title":"Stone duality and Gleason covers through de Vries duality","volume":"157","author":"Bezhanishvili","year":"2010","journal-title":"Topology and its Applications"},{"key":"2025090809271429400_ref3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/logcom\/exs030","article-title":"Modal compact Hausdorff spaces","volume":"25","author":"Bezhanishvili","year":"2015","journal-title":"Journal of Logic and Computation"},{"key":"2025090809271429400_ref4","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1017\/jsl.2015.54","article-title":"Stable canonical rules","volume":"81","author":"Bezhanishvili","year":"2016","journal-title":"Journal of Symbolic Logic"},{"key":"2025090809271429400_ref5","doi-asserted-by":"crossref","first-page":"102714","DOI":"10.1016\/j.apal.2019.06.003","article-title":"A strict implication calculus for compact Hausdorff spaces","volume":"170","author":"Bezhanishvili","year":"2019","journal-title":"Annals of Pure and Applied Logic"},{"key":"2025090809271429400_ref6","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/s10485-016-9434-2","article-title":"Irreducible equivalence relations, Gleason spaces, and de Vries duality","volume":"25","author":"Bezhanishvili","year":"2017","journal-title":"Applied Categorical Structures"},{"key":"2025090809271429400_ref7","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1007\/s10485-019-09573-x","article-title":"Compact Hausdorff spaces with relations and Gleason spaces","volume":"27","author":"Bezhanishvili","year":"2019","journal-title":"Applied Categorical Structures"},{"key":"2025090809271429400_ref8","doi-asserted-by":"crossref","first-page":"103169","DOI":"10.1016\/j.apal.2022.103169","article-title":"Admissibility of $\\Pi_2$-inference rules: Interpolation, model completion, and contact algebras","volume":"174","author":"Bezhanishvili","year":"2023","journal-title":"Annals of Pure and Applied Logic"},{"key":"2025090809271429400_ref9","first-page":"115","article-title":"Model completeness and $\\Pi_2$-rules: the case of contact algebras","volume-title":"13th Conference on Advances in Modal Logic, AiML 2020, Helsinki, Finland, August 24\u201328, 2020","author":"Bezhanishvili","year":"2020"},{"volume-title":"Modal Logic, Volume 53 of Cambridge Tracts in Theoretical Computer Science","year":"2001","author":"Blackburn","key":"2025090809271429400_ref10"},{"key":"2025090809271429400_ref11","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BF00370320","article-title":"Decidability for branching time","volume":"39","author":"Burgess","year":"1980","journal-title":"Studia Logica"},{"volume-title":"Modal Logic, Volume 35 of Oxford Logic Guides","year":"1997","author":"Chagrov","key":"2025090809271429400_ref12"},{"key":"2025090809271429400_ref13","first-page":"1","article-title":"Algorithmic correspondence and completeness in modal logic. 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