{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T09:42:24Z","timestamp":1759398144947,"version":"build-2065373602"},"publisher-location":"Singapore","reference-count":25,"publisher":"Springer Nature Singapore","isbn-type":[{"value":"9789819524808","type":"print"},{"value":"9789819524815","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,10,3]],"date-time":"2025-10-03T00:00:00Z","timestamp":1759449600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,10,3]],"date-time":"2025-10-03T00:00:00Z","timestamp":1759449600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-981-95-2481-5_12","type":"book-chapter","created":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T09:06:58Z","timestamp":1759396018000},"page":"165-178","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Finite Model Property in\u00a0Normal Extensions of\u00a0Euclidean Quasi-Boolean Modal Logics"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5975-2333","authenticated-orcid":false,"given":"Yiheng","family":"Wang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6371-9862","authenticated-orcid":false,"given":"Yu","family":"Peng","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,10,3]]},"reference":[{"issue":"3","key":"12_CR1","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1093\/jigpal\/jzab036","volume":"31","author":"M Alizadeh","year":"2023","unstructured":"Alizadeh, M., Ardeshir, M., Balbiani, P., Mojtahedi, M.: Unification types in Euclidean modal logics. Logic J. IGPL 31(3), 422\u2013440 (2023)","journal-title":"Logic J. IGPL"},{"key":"12_CR2","doi-asserted-by":"crossref","unstructured":"Belnap, N.: A useful four-valued logic. In: Dunn, M., Epstein, G. (eds.) Modern Uses of Multiple-valued Logic, pp. 5\u201337. Springer (1977)","DOI":"10.1007\/978-94-010-1161-7_2"},{"key":"12_CR3","unstructured":"Bia\u0142ynicki-Birula, A., Rasiowa, H.: On the representation of quasi-Boolean algebras. Bull. Polish Acad. Sci. Cl. III 5(3), 259\u2013261 (1957)"},{"key":"12_CR4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107050884","volume-title":"Modal Logic","author":"P Blackburn","year":"2001","unstructured":"Blackburn, P., Rijke, M., Venema, Y.: Modal Logic, vol. 53. Cambridge University Press, Cambridge, UK (2001)"},{"issue":"1","key":"12_CR5","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/s11225-011-9328-0","volume":"98","author":"SA Celani","year":"2011","unstructured":"Celani, S.A.: Classical modal De Morgan algebras. Stud. Logica. 98(1), 251\u2013266 (2011)","journal-title":"Stud. Logica."},{"key":"12_CR6","unstructured":"Celani, S.A.: L\u00f3gicas modales distributivas y de De Morgan. Ph.D. thesis, Universidad de Barcelona (1995)"},{"key":"12_CR7","doi-asserted-by":"crossref","unstructured":"Chagrov, A., Zakharyaschev, M.: Modal Logic. Clarendon Press (1997)","DOI":"10.1093\/oso\/9780198537793.001.0001"},{"issue":"4","key":"12_CR8","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1305\/ndjfl\/1093870147","volume":"23","author":"JM Dunn","year":"1982","unstructured":"Dunn, J.M.: A relational representation of quasi-Boolean algebras. Notre Dame J. Formal Logic 23(4), 353\u2013357 (1982)","journal-title":"Notre Dame J. Formal Logic"},{"issue":"2","key":"12_CR9","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/BF01061239","volume":"55","author":"JM Dunn","year":"1995","unstructured":"Dunn, J.M.: Positive modal logic. Stud. Logica. 55(2), 301\u2013317 (1995)","journal-title":"Stud. Logica."},{"key":"12_CR10","unstructured":"Dunn, J.M.: The algebra of intensional logics. Ph.D. thesis, University of Pittsburgh (1966)"},{"key":"12_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1007\/11828563_11","volume-title":"Relations and Kleene Algebra in Computer Science","author":"W Dzik","year":"2006","unstructured":"Dzik, W., Orlowska, E., Alten, C.: Relational representation theorems for general lattices with negations. In: Schmidt, R.A. (ed.) RelMiCS 2006. LNCS, vol. 4136, pp. 162\u2013176. Springer, Heidelberg (2006). https:\/\/doi.org\/10.1007\/11828563_11"},{"issue":"3","key":"12_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1093\/jigpal\/5.3.1-e","volume":"5","author":"JM Font","year":"1997","unstructured":"Font, J.M.: Belnap\u2019s four-valued logic and De Morgan lattices. Log. J. IGPL 5(3), 1\u201329 (1997)","journal-title":"Log. J. IGPL"},{"issue":"01","key":"12_CR13","doi-asserted-by":"publisher","first-page":"1950010","DOI":"10.1142\/S1793557119500104","volume":"12","author":"V Gregori","year":"2019","unstructured":"Gregori, V.: Discrete duality for De Morgan algebras with operators. Asian-Eur. J. Math. 12(01), 1950010 (2019)","journal-title":"Asian-Eur. J. Math."},{"key":"12_CR14","unstructured":"Hintikka, J.: Knowledge and Belief: An Introduction to the Logic of the Two Notions. Cornell University Press (1962)"},{"key":"12_CR15","unstructured":"Lenzen, W.: Recent work in epistemic logic. Acta Philosophica Fennica 30 (1978)"},{"key":"12_CR16","doi-asserted-by":"crossref","unstructured":"Ma, M., Guo, J.: Kripke-completeness and sequent calculus for quasi-Boolean modal logic. Studia Logica 1\u201330 (2024)","DOI":"10.1007\/s11225-024-10095-4"},{"issue":"2","key":"12_CR17","doi-asserted-by":"publisher","first-page":"319","DOI":"10.2307\/2273624","volume":"46","author":"MC Nagle","year":"1981","unstructured":"Nagle, M.C.: The decidability of normal K5 logics. J. Symbolic Logic 46(2), 319\u2013328 (1981)","journal-title":"J. Symbolic Logic"},{"key":"12_CR18","unstructured":"Nagle, M.C.: Normal K5 Logics. Ph.D. thesis, University of Calgary (1981)"},{"issue":"1","key":"12_CR19","doi-asserted-by":"publisher","first-page":"102","DOI":"10.2307\/2273793","volume":"50","author":"MC Nagle","year":"1985","unstructured":"Nagle, M.C., Thomason, S.K.: The extensions of the modal logic K5. J. Symbolic Logic 50(1), 102\u2013109 (1985)","journal-title":"J. Symbolic Logic"},{"issue":"3","key":"12_CR20","doi-asserted-by":"publisher","first-page":"279","DOI":"10.3166\/jancl.20.279-304","volume":"20","author":"SP Odintsov","year":"2010","unstructured":"Odintsov, S.P., Wansing, H.: Modal logics with Belnapian truth values. J. Appl. Non-Classical Logics 20(3), 279\u2013301 (2010)","journal-title":"J. Appl. Non-Classical Logics"},{"key":"12_CR21","volume-title":"An Algebraic Approach to Non-classical Logics, Studies in logic and the foundations of mathematics","author":"H Rasiowa","year":"1974","unstructured":"Rasiowa, H.: An Algebraic Approach to Non-classical Logics, Studies in logic and the foundations of mathematics, vol. 78. PWN-Polish Scientific Publishers, Warszawa (1974)"},{"key":"12_CR22","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1016\/j.ins.2014.06.004","volume":"282","author":"A Saha","year":"2014","unstructured":"Saha, A., Sen, J., Chakraborty, M.K.: Algebraic structures in the vicinity of pre-rough algebra and their logics I. Inf. Sci. 282, 296\u2013320 (2014)","journal-title":"Inf. Sci."},{"issue":"527","key":"12_CR23","doi-asserted-by":"publisher","first-page":"605","DOI":"10.1093\/mind\/fzac048","volume":"132","author":"WK San","year":"2023","unstructured":"San, W.K.: KK, knowledge, knowability. Mind 132(527), 605\u2013630 (2023)","journal-title":"Mind"},{"issue":"2","key":"12_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2022.103202","volume":"174","author":"V Shehtman","year":"2023","unstructured":"Shehtman, V.: On Kripke completeness of modal predicate logics around quantified K5. Ann. Pure Appl. Logic 174(2), 103202 (2023)","journal-title":"Ann. Pure Appl. Logic"},{"issue":"2\u20133","key":"12_CR25","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1080\/11663081.2024.2336373","volume":"34","author":"Y Wang","year":"2024","unstructured":"Wang, Y., Lin, Z., Ma, M.: Decidability of topological quasi-Boolean algebras. J. Appl. Non-Classical Logics 34(2\u20133), 269\u2013293 (2024)","journal-title":"J. Appl. Non-Classical Logics"}],"container-title":["Lecture Notes in Computer Science","Logic, Rationality, and Interaction"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-95-2481-5_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T09:07:07Z","timestamp":1759396027000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-95-2481-5_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,3]]},"ISBN":["9789819524808","9789819524815"],"references-count":25,"URL":"https:\/\/doi.org\/10.1007\/978-981-95-2481-5_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,3]]},"assertion":[{"value":"3 October 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"LORI","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Logic, Rationality and Interaction","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Xi\u2019an","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"China","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 October 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 October 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"lori2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/golori.org\/lori2025\/index.html","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}