{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T16:53:23Z","timestamp":1773939203609,"version":"3.50.1"},"publisher-location":"Cham","reference-count":22,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031509582","type":"print"},{"value":"9783031509599","type":"electronic"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"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":[[2023]]},"DOI":"10.1007\/978-3-031-50959-9_11","type":"book-chapter","created":{"date-parts":[[2023,12,30]],"date-time":"2023-12-30T10:02:35Z","timestamp":1703930555000},"page":"154-169","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Two-Sorted Modal Logic for\u00a0Formal and\u00a0Rough Concepts"],"prefix":"10.1007","author":[{"given":"Prosenjit","family":"Howlader","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Churn-Jung","family":"Liau","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,12,31]]},"reference":[{"issue":"3","key":"11_CR1","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1016\/j.jal.2012.04.003","volume":"10","author":"P Balbiani","year":"2012","unstructured":"Balbiani, P.: Deciding the word problem in pure double Boolean algebras. J. Appl. Log. 10(3), 260\u2013273 (2012)","journal-title":"J. Appl. Log."},{"key":"11_CR2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107050884","volume-title":"Modal Logic","author":"P Blackburn","year":"2001","unstructured":"Blackburn, P., De Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)"},{"key":"11_CR3","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1016\/j.ins.2020.05.074","volume":"561","author":"W Conradie","year":"2021","unstructured":"Conradie, W., et al.: Rough concepts. Inf. Sci. 561, 371\u2013413 (2021)","journal-title":"Inf. Sci."},{"key":"11_CR4","doi-asserted-by":"crossref","unstructured":"D\u00fcntsch, I., Gediga, G.: Modal-style operators in qualitative data analysis. In: Vipin, K., et al. (eds.) Proceedings of the 2002 IEEE International Conference on Data Mining, pp. 155\u2013162. IEEE Computer Society (2002)","DOI":"10.1109\/ICDM.2002.1183898"},{"key":"11_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/978-3-642-21563-6_3","volume-title":"Transactions on Rough Sets XIV","author":"B Ganter","year":"2011","unstructured":"Ganter, B., Meschke, C.: A formal concept analysis approach to rough data tables. In: Peters, J.F., et al. (eds.) Transactions on Rough Sets XIV. LNCS, vol. 6600, pp. 37\u201361. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-21563-6_3"},{"key":"11_CR6","doi-asserted-by":"publisher","unstructured":"Gargov, G., Passy, S., Tinchev, T.: Modal environment for Boolean speculations. In: Skordev, D.G. (eds) Mathematical Logic and Its Applications, pp. 253\u2013263, Springer, Boston (1987). https:\/\/doi.org\/10.1007\/978-1-4613-0897-3_17","DOI":"10.1007\/978-1-4613-0897-3_17"},{"key":"11_CR7","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/s10849-022-09370-1","volume":"32","author":"P Howlader","year":"2023","unstructured":"Howlader, P., Banerjee, M.: Kripke contexts, double Boolean algebras with operators and corresponding modal systems. J. Logic Lang. Inform. 32, 117\u2013146 (2023)","journal-title":"J. Logic Lang. Inform."},{"key":"11_CR8","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/j.ijar.2022.11.015","volume":"153","author":"P Howlader","year":"2023","unstructured":"Howlader, P., Banerjee, M.: A non-distributive logic for semiconcepts and its modal extension with semantics based on Kripke contexts. Int. J. Approximate Reasoning 153, 115\u2013143 (2023)","journal-title":"Int. J. Approximate Reasoning"},{"key":"11_CR9","doi-asserted-by":"crossref","unstructured":"Howlader, P., Banerjee, M.: Topological representation of double Boolean algebras. Algebra Univer. 84, Paper No. 15, 32 (2023)","DOI":"10.1007\/s00012-023-00811-x"},{"key":"11_CR10","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/3-540-45357-1_21","volume-title":"Advances in Knowledge Discovery and Data Mining","author":"K Hu","year":"2001","unstructured":"Hu, K., Sui, Y., Lu, Y., Wang, J., Shi, C.: Concept approximation in concept lattice. In: Cheung, D., Williams, G.J., Li, Q. (eds.) PAKDD 2001. LNCS (LNAI), vol. 2035, pp. 167\u2013173. Springer, Heidelberg (2001). https:\/\/doi.org\/10.1007\/3-540-45357-1_21"},{"key":"11_CR11","doi-asserted-by":"publisher","unstructured":"Kent, R.E.: Rough concept analysis. In: Ziarko, W.P. (ed.) Rough Sets. Fuzzy Sets and Knowledge Discovery, pp. 248\u2013255. Springer, London (1994). https:\/\/doi.org\/10.1007\/978-1-4471-3238-7_30","DOI":"10.1007\/978-1-4471-3238-7_30"},{"key":"11_CR12","doi-asserted-by":"crossref","unstructured":"Leu\u015ftean, L., Moang\u0103, N., \u015eerb\u0103nu\u0163\u0103, T.F.: A many-sorted polyadic modal logic. Fund. Inform. 173(2\u20133), 191\u2013215 (2020)","DOI":"10.3233\/FI-2020-1921"},{"key":"11_CR13","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1007\/978-3-642-11928-6_8","volume-title":"Formal Concept Analysis","author":"C Meschke","year":"2010","unstructured":"Meschke, C.: Approximations in concept lattices. In: Kwuida, L., Sertkaya, B. (eds.) ICFCA 2010. LNCS (LNAI), vol. 5986, pp. 104\u2013123. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-11928-6_8"},{"issue":"5","key":"11_CR14","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/BF01001956","volume":"11","author":"Z Pawlak","year":"1982","unstructured":"Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11(5), 341\u2013356 (1982)","journal-title":"Int. J. Comput. Inform. Sci."},{"key":"11_CR15","unstructured":"Saquer, J., Deogun, J.S.: Concept approximations based on rough sets and similarity measures. Int. J. Appl. Math. Comput. Sci. 11(3), 655\u2013674 (2001)"},{"key":"11_CR16","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1007\/11528784_2","volume-title":"Formal Concept Analysis","author":"B Vormbrock","year":"2005","unstructured":"Vormbrock, B., Wille, R.: Semiconcept and protoconcept algebras: the basic theorems. In: Ganter, B., Stumme, G., Wille, R. (eds.) Formal Concept Analysis. LNCS (LNAI), vol. 3626, pp. 34\u201348. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/11528784_2"},{"key":"11_CR17","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"314","DOI":"10.1007\/978-3-642-01815-2_23","volume-title":"Formal Concept Analysis","author":"R Wille","year":"2009","unstructured":"Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Ferr\u00e9, S., Rudolph, S. (eds.) ICFCA 2009. LNCS (LNAI), vol. 5548, pp. 314\u2013339. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-01815-2_23"},{"key":"11_CR18","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1007\/10722280_22","volume-title":"Conceptual Structures: Logical, Linguistic, and Computational Issues","author":"R Wille","year":"2000","unstructured":"Wille, R.: Boolean concept logic. In: Ganter, B., Mineau, G.W. (eds.) ICCS-ConceptStruct 2000. LNCS (LNAI), vol. 1867, pp. 317\u2013331. Springer, Heidelberg (2000). https:\/\/doi.org\/10.1007\/10722280_22"},{"key":"11_CR19","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/978-3-540-25929-9_6","volume-title":"Rough Sets and Current Trends in Computing","author":"Y Yao","year":"2004","unstructured":"Yao, Y.: A comparative study of formal concept analysis and rough set theory in data analysis. In: Tsumoto, S., S\u0142owi\u0144ski, R., Komorowski, J., Grzyma\u0142a-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 59\u201368. Springer, Heidelberg (2004). https:\/\/doi.org\/10.1007\/978-3-540-25929-9_6"},{"key":"11_CR20","doi-asserted-by":"crossref","unstructured":"Yao, Y.Y.: Concept lattices in rough set theory. In: IEEE Annual Meeting of the Fuzzy Information Processing Society-NAFIPS, vol. 2, pp. 796\u2013801. IEEE (2004)","DOI":"10.1109\/NAFIPS.2004.1337404"},{"key":"11_CR21","doi-asserted-by":"crossref","unstructured":"Yao, Y.Y., Chen, Y.: Rough set approximations in formal concept analysis. In: Peters, J.F., et al. (eds.) Transactions on Rough Sets V, pp. 285\u2013305. Springer, Berlin (2006)","DOI":"10.1007\/11847465_14"},{"issue":"2","key":"11_CR22","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1080\/10798587.1996.10750660","volume":"2","author":"YY Yao","year":"1996","unstructured":"Yao, Y.Y., Lin, T.Y.: Generalization of rough sets using modal logics. Intell. Autom. Soft Comput. 2(2), 103\u2013119 (1996)","journal-title":"Intell. Autom. Soft Comput."}],"container-title":["Lecture Notes in Computer Science","Rough Sets"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-50959-9_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,7]],"date-time":"2024-11-07T03:13:41Z","timestamp":1730949221000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-50959-9_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031509582","9783031509599"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-50959-9_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"31 December 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"IJCRS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Joint Conference on Rough Sets","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Krakow","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Poland","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5 October 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 October 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ijcrs2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/ijcrs2023.agh.edu.pl\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Springer EquinOCS","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"83","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"43","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"52% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"5","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}