{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T02:31:45Z","timestamp":1775097105884,"version":"3.50.1"},"publisher-location":"Cham","reference-count":26,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030388072","type":"print"},{"value":"9783030388089","type":"electronic"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-38808-9_9","type":"book-chapter","created":{"date-parts":[[2020,1,13]],"date-time":"2020-01-13T17:03:25Z","timestamp":1578935005000},"page":"141-154","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Iterative Division in the Distributive Full Non-associative Lambek Calculus"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1942-7982","authenticated-orcid":false,"given":"Igor","family":"Sedl\u00e1r","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,1,14]]},"reference":[{"key":"9_CR1","doi-asserted-by":"crossref","unstructured":"van Benthem, J.: A note on dynamic arrow logic. In: van Eijck, J., Visser, A. (eds.) Logic and Information Flow, pp. 15\u201329. MIT Press (1994)","DOI":"10.7551\/mitpress\/4286.003.0004"},{"key":"9_CR2","doi-asserted-by":"publisher","first-page":"693","DOI":"10.1016\/S0049-237X(06)80070-4","volume-title":"Logic, Methodology and Philosophy of Science IX, Proceedings of the Ninth International Congress of Logic, Methodology and Philosophy of Science","author":"Johan van Benthem","year":"1995","unstructured":"van Benthem, J.: Logic and the flow of information. In: Prawitz, D., Skyrms, B., Westerst\u0227hl, D. (eds.) Logic, Methodology and Philosophy of Science IX, Studies in Logic and the Foundations of Mathematics, vol. 134, pp. 693\u2013724. Elsevier (1995). https:\/\/doi.org\/10.1016\/S0049-237X(06)80070-4"},{"key":"9_CR3","series-title":"Outstanding Contributions to Logic","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/978-94-007-7046-1_13","volume-title":"Krister Segerberg on Logic of Actions","author":"J Benthem","year":"2014","unstructured":"Benthem, J.: Two logical faces of belief revision. In: Trypuz, R. (ed.) Krister Segerberg on Logic of Actions. OCL, vol. 1, pp. 281\u2013300. Springer, Dordrecht (2014). https:\/\/doi.org\/10.1007\/978-94-007-7046-1_13"},{"issue":"4","key":"9_CR4","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1305\/ndjfl\/1134397663","volume":"46","author":"K Bimb\u00f3","year":"2005","unstructured":"Bimb\u00f3, K., Dunn, J.M.: Relational semantics for Kleene logic and action logic. Notre Dame J. Formal Logic 46(4), 461\u2013490 (2005). https:\/\/doi.org\/10.1305\/ndjfl\/1134397663","journal-title":"Notre Dame J. Formal Logic"},{"issue":"1","key":"9_CR5","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1093\/logcom\/exl036","volume":"17","author":"W Buszkowski","year":"2006","unstructured":"Buszkowski, W.: On action logic: equational theories of action algebras. J. Logic Comput. 17(1), 199\u2013217 (2006). https:\/\/doi.org\/10.1093\/logcom\/exl036","journal-title":"J. Logic Comput."},{"key":"9_CR6","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511621192","volume-title":"Modal Logic. An Introduction","author":"B Chellas","year":"1980","unstructured":"Chellas, B.: Modal Logic. An Introduction. Cambridge University Press, Cambridge (1980)"},{"key":"9_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/978-3-319-57418-9_6","volume-title":"Relational and Algebraic Methods in Computer Science","author":"J Desharnais","year":"2017","unstructured":"Desharnais, J., M\u00f6ller, B.: Non-associative Kleene algebra and temporal logics. In: H\u00f6fner, P., Pous, D., Struth, G. (eds.) RAMICS 2017. LNCS, vol. 10226, pp. 93\u2013108. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-57418-9_6"},{"issue":"1","key":"9_CR8","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1002\/malq.19920380113","volume":"38","author":"K Do\u0161en","year":"1992","unstructured":"Do\u0161en, K.: A brief survey of frames for the Lambek Calculus. Math. Logic Q. 38(1), 179\u2013187 (1992). https:\/\/doi.org\/10.1002\/malq.19920380113","journal-title":"Math. Logic Q."},{"key":"9_CR9","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/2516.001.0001","volume-title":"Dynamic Logic","author":"D Harel","year":"2000","unstructured":"Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)"},{"key":"9_CR10","unstructured":"Holliday, W.H., Hoshi, T., Icard III, T.F.: A uniform logic of information dynamics. In: Bolander, T., Bra\u00fcner, T., Ghilardi, S., Moss, L. (eds.) Advances in Modal Logic 2012, pp. 348\u2013367. College Publications (2012)"},{"issue":"2","key":"9_CR11","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1006\/inco.1994.1037","volume":"110","author":"D Kozen","year":"1994","unstructured":"Kozen, D.: A completeness theorem for Kleene algebras and the algebra of regular events. Inf. Comput. 110(2), 366\u2013390 (1994). https:\/\/doi.org\/10.1006\/inco.1994.1037","journal-title":"Inf. Comput."},{"key":"9_CR12","doi-asserted-by":"crossref","unstructured":"Kozen, D.: On action algebras. In: Logic and Information Flow, pp. 78\u201388. MIT Press (1994)","DOI":"10.7551\/mitpress\/4286.003.0007"},{"key":"9_CR13","unstructured":"Kurtonina, N.: Frames and labels. A modal analysis of categorial inference. Ph.D. thesis, Utrecht University (1994)"},{"issue":"3","key":"9_CR14","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/BF01049412","volume":"4","author":"\u00c1 Kurucz","year":"1995","unstructured":"Kurucz, \u00c1., N\u00e9meti, I., Sain, I., Simon, A.: Decidable and undecidable logics with a binary modality. J. Logic Lang. Inf. 4(3), 191\u2013206 (1995). https:\/\/doi.org\/10.1007\/BF01049412","journal-title":"J. Logic Lang. Inf."},{"key":"9_CR15","doi-asserted-by":"publisher","unstructured":"Kuznetsov, S.: The logic of action lattices is undecidable. In: 34th Annual ACM\/IEEE Symposium on Logic in Computer Science, LICS 2019, Vancouver, BC, Canada, 24\u201327 June 2019, pp. 1\u20139 (2019). https:\/\/doi.org\/10.1109\/LICS.2019.8785659","DOI":"10.1109\/LICS.2019.8785659"},{"issue":"3","key":"9_CR16","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1080\/00029890.1958.11989160","volume":"65","author":"J Lambek","year":"1958","unstructured":"Lambek, J.: The mathematics of sentence structure. Am. Math. Mon. 65(3), 154\u2013170 (1958)","journal-title":"Am. Math. Mon."},{"key":"9_CR17","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1090\/psapm\/012\/9972","volume-title":"Structure of Language and Its Mathematical Aspects","author":"J Lambek","year":"1961","unstructured":"Lambek, J.: On the calculus of syntactic types. In: Jakobson, R. (ed.) Structure of Language and Its Mathematical Aspects, pp. 166\u2013178. AMS, Providence (1961)"},{"issue":"3","key":"9_CR18","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/BF00159344","volume":"5","author":"MJ Moortgat","year":"1996","unstructured":"Moortgat, M.J.: Multimodal linguistic inference. J. Logic Lang. Inf. 5(3), 349\u2013385 (1996). https:\/\/doi.org\/10.1007\/BF00159344","journal-title":"J. Logic Lang. Inf."},{"issue":"2","key":"9_CR19","doi-asserted-by":"publisher","first-page":"847","DOI":"10.2977\/prims\/1195183579","volume":"18","author":"H Nishimura","year":"1982","unstructured":"Nishimura, H.: Semantical analysis of constructive PDL. Publ. Res. Inst. Math. Sci. 18(2), 847\u2013858 (1982). https:\/\/doi.org\/10.2977\/prims\/1195183579","journal-title":"Publ. Res. Inst. Math. Sci."},{"issue":"2","key":"9_CR20","first-page":"295","volume":"78","author":"E Palka","year":"2007","unstructured":"Palka, E.: An infinitary sequent system for the equational theory of *-continuous action lattices. Fundamenta Informaticae 78(2), 295\u2013309 (2007)","journal-title":"Fundamenta Informaticae"},{"key":"9_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/BFb0018436","volume-title":"Logics in AI","author":"V Pratt","year":"1991","unstructured":"Pratt, V.: Action logic and pure induction. In: van Eijck, J. (ed.) JELIA 1990. LNCS, vol. 478, pp. 97\u2013120. Springer, Heidelberg (1991). https:\/\/doi.org\/10.1007\/BFb0018436"},{"key":"9_CR22","volume-title":"An Introduction to Substrucutral Logics","author":"G Restall","year":"2000","unstructured":"Restall, G.: An Introduction to Substrucutral Logics. Routledge, London (2000)"},{"key":"9_CR23","unstructured":"Segerberg, K.: An Essay in Classical Modal Logic. Filosofiska F\u00f6reningen Och Filosofiska Institutionen Vid Uppsala Universitet, Uppsala (1971)"},{"issue":"1","key":"9_CR24","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/s11229-010-9834-z","volume":"190","author":"S Sequoiah-Grayson","year":"2013","unstructured":"Sequoiah-Grayson, S.: Epistemic closure and commutative, nonassociative residuated structures. Synthese 190(1), 113\u2013128 (2013). https:\/\/doi.org\/10.1007\/s11229-010-9834-z","journal-title":"Synthese"},{"issue":"3","key":"9_CR25","first-page":"731","volume":"4","author":"A Tedder","year":"2017","unstructured":"Tedder, A.: Channel composition and ternary relation semantics. IFCoLog J. Logics Appl. 4(3), 731\u2013735 (2017)","journal-title":"IFCoLog J. Logics Appl."},{"key":"9_CR26","first-page":"3","volume-title":"Arrow Logic and Multi-Modal Logic","author":"Y Venema","year":"1997","unstructured":"Venema, Y.: A crash course in arrow logic. In: Marx, M., P\u00f3los, L., Masuch, M. (eds.) Arrow Logic and Multi-Modal Logic, pp. 3\u201334. Center for the Study of Language and Information, Stanford (1997)"}],"container-title":["Lecture Notes in Computer Science","Dynamic Logic. New Trends and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-38808-9_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T01:47:59Z","timestamp":1722304079000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-38808-9_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030388072","9783030388089"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-38808-9_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"14 January 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"DALI","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Dynamic Logic","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Porto","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Portugal","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7 October 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 October 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"dali2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/workshop.dali.di.uminho.pt\/","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":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"26","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":"12","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":"2","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":"46% - 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":"2","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":"No","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}