{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T00:05:33Z","timestamp":1759017933036,"version":"3.44.0"},"publisher-location":"Cham","reference-count":32,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032060846","type":"print"},{"value":"9783032060853","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T00:00:00Z","timestamp":1758758400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T00:00:00Z","timestamp":1758758400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>We consider a family of non-classical three-valued logics proposed to model <jats:italic>indicative conditionals<\/jats:italic> in natural language. Among these, systems introduced by B.\u00a0De Finetti, W.S.\u00a0Cooper, J.\u00a0Cantwell and R.J.\u00a0Farrell, as well as some variants that have not appeared in the literature, but seem nevertheless to be natural objects of interest from a formal point of view. Most of these logics are not easily treatable with the standard techniques of algebraic logic. We therefore resort to non-deterministic structures and multiple-conclusion calculi to provide alternative semantical characterizations and axiomatizations. In the best cases\u2014logics given by a finite monadic matrix\u2014this can be done directly, in a modular way, through a procedure due to Shoesmith and Smiley. In the more involved ones\u2014logics preserving degrees of truth\u2014some ingenuity and more sophisticated techniques are required. We characterize these logics by a partial non-deterministic matrix, and show how to produce analytic (and effective) calculi that are complete with respect to this generalized semantics. In all cases, the calculi thus obtained can be straightforwardly converted, by a uniform procedure, into traditional single-conclusion Hilbert-style axiomatizations.<\/jats:p>","DOI":"10.1007\/978-3-032-06085-3_4","type":"book-chapter","created":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T10:45:09Z","timestamp":1758969909000},"page":"59-81","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analytic Calculi for\u00a0Logics of\u00a0Indicative Conditionals"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3240-386X","authenticated-orcid":false,"given":"Vitor","family":"Greati","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6941-7555","authenticated-orcid":false,"given":"S\u00e9rgio","family":"Marcelino","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0001-3468-8208","authenticated-orcid":false,"given":"Miguel","family":"Mu\u00f1oz P\u00e9rez","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1364-5003","authenticated-orcid":false,"given":"Umberto","family":"Rivieccio","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,9,25]]},"reference":[{"issue":"6","key":"4_CR1","doi-asserted-by":"publisher","first-page":"1051","DOI":"10.1007\/s11225-017-9739-7","volume":"105","author":"H Albuquerque","year":"2017","unstructured":"Albuquerque, H., P\u0159enosil, A., Rivieccio, U.: An algebraic view of super-Belnap logics. Stud. Log. 105(6), 1051\u20131086 (2017). https:\/\/doi.org\/10.1007\/s11225-017-9739-7","journal-title":"Stud. Log."},{"issue":"1","key":"4_CR2","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s11787-006-0003-6","volume":"1","author":"A Avron","year":"2007","unstructured":"Avron, A., Ben-Naim, J., Konikowska, B.: Cut-free ordinary sequent calculi for logics having generalized finite-valued semantics. Log. Univers. 1(1), 41\u201370 (2007). https:\/\/doi.org\/10.1007\/s11787-006-0003-6","journal-title":"Log. Univers."},{"issue":"4","key":"4_CR3","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1093\/jigpal\/jzi030","volume":"13","author":"A Avron","year":"2005","unstructured":"Avron, A., Konikowska, B.: Multi-valued calculi for logics based on non-determinism. Log. J. IGPL 13(4), 365\u2013387 (2005). https:\/\/doi.org\/10.1093\/jigpal\/jzi030","journal-title":"Log. J. IGPL"},{"issue":"4","key":"4_CR4","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/s10817-013-9273-x","volume":"51","author":"M Baaz","year":"2013","unstructured":"Baaz, M., Lahav, O., Zamansky, A.: Finite-valued semantics for canonical labelled calculi. J. Autom. Reason. 51(4), 401\u2013430 (2013). https:\/\/doi.org\/10.1007\/s10817-013-9273-x","journal-title":"J. Autom. Reason."},{"key":"4_CR5","doi-asserted-by":"crossref","unstructured":"Baaz, M., Ferm\u00fcller, C.G., Salzer, G.: Automated Deduction for Many-Valued Logics, p. 1355\u20131402. Elsevier Science Publishers B. V., NLD (2001)","DOI":"10.1016\/B978-044450813-3\/50022-9"},{"key":"4_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1007\/978-3-662-59533-6_6","volume-title":"Logic, Language, Information, and Computation","author":"C Caleiro","year":"2019","unstructured":"Caleiro, C., Marcelino, S.: Analytic calculi for monadic PNmatrices. In: Iemhoff, R., Moortgat, M., de Queiroz, R. (eds.) WoLLIC 2019. LNCS, vol. 11541, pp. 84\u201398. Springer, Heidelberg (2019). https:\/\/doi.org\/10.1007\/978-3-662-59533-6_6"},{"key":"4_CR7","doi-asserted-by":"publisher","unstructured":"Caleiro, C., Marcelino, S.: Modular many-valued semantics for combined logics. J. Symb. Log. 1\u201354 (2023). https:\/\/doi.org\/10.1017\/jsl.2023.22","DOI":"10.1017\/jsl.2023.22"},{"issue":"3","key":"4_CR8","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1215\/00294527-2008-010","volume":"49","author":"J Cantwell","year":"2008","unstructured":"Cantwell, J.: The logic of conditional negation. Notre Dame J. Formal Log. 49(3), 245\u2013260 (2008). https:\/\/doi.org\/10.1215\/00294527-2008-010","journal-title":"Notre Dame J. Formal Log."},{"key":"4_CR9","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1007\/BF01230621","volume":"23","author":"R Cignoli","year":"1986","unstructured":"Cignoli, R.: The class of Kleene algebras satisfying an interpolation property and nelson algebras. Algebra Univers. 23, 262\u2013292 (1986). https:\/\/doi.org\/10.1007\/BF01230621","journal-title":"Algebra Univers."},{"key":"4_CR10","doi-asserted-by":"publisher","unstructured":"Cooper, W.S.: The propositional logic of ordinary discourse. Inq.: Interdisc. J. Philos. 11(1-4), 295\u2013320 (1968). https:\/\/doi.org\/10.1080\/00201746808601531","DOI":"10.1080\/00201746808601531"},{"issue":"2","key":"4_CR11","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/s10992-020-09549-6","volume":"50","author":"P \u00c9gr\u00e9","year":"2020","unstructured":"\u00c9gr\u00e9, P., Rossi, L., Sprenger, J.: De Finettian logics of indicative conditionals part I: trivalent semantics and validity. J. Philos. Log. 50(2), 187\u2013213 (2020). https:\/\/doi.org\/10.1007\/s10992-020-09549-6","journal-title":"J. Philos. Log."},{"key":"4_CR12","unstructured":"Egr\u00e9, P., Rossi, L., Spengler, J.: Certain and uncertain inference with indicative conditionals. Preprint available at the arXiv (2023)"},{"issue":"2","key":"4_CR13","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/s10992-020-09572-7","volume":"50","author":"P \u00c9gr\u00e9","year":"2021","unstructured":"\u00c9gr\u00e9, P., Rossi, L., Sprenger, J.: De Finettian logics of indicative conditionals part II: proof theory and algebraic semantics. J. Philos. Log. 50(2), 215\u2013247 (2021). https:\/\/doi.org\/10.1007\/s10992-020-09572-7","journal-title":"J. Philos. Log."},{"key":"4_CR14","doi-asserted-by":"crossref","unstructured":"Farrell, R.J.: Implication and presupposition. Notre Dame J. Formal Log. 27(1) (1986)","DOI":"10.1305\/ndjfl\/1093636522"},{"issue":"2","key":"4_CR15","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1305\/ndjfl\/1093882546","volume":"20","author":"RJ Farrell","year":"1979","unstructured":"Farrell, R.J.: Material implication, confirmation, and counterfactuals. Notre Dame J. Formal Log. 20(2), 383\u2013394 (1979)","journal-title":"Notre Dame J. Formal Log."},{"key":"4_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-023-10057-2","author":"D Fazio","year":"2023","unstructured":"Fazio, D., Odintsov, S.P.: An algebraic investigation of the connexive logic C. Stud. Log. (2023). https:\/\/doi.org\/10.1007\/s11225-023-10057-2","journal-title":"Stud. Log."},{"key":"4_CR17","doi-asserted-by":"crossref","unstructured":"de\u00a0Finetti, B.: La logique de la probabilit\u00e9. In: Actes du Congr\u00e9s International de Philosophie Scientifique (1936)","DOI":"10.5840\/icus11936454"},{"key":"4_CR18","unstructured":"Font, J.M., Jansana, R.: A General Algebraic Semantics for Sentential Logics. Springer, Cham (2009)"},{"key":"4_CR19","unstructured":"Font, J.M.: Abstract Algebraic Logic: An introductory textbook. College Publications (2016)"},{"key":"4_CR20","doi-asserted-by":"crossref","unstructured":"Greati, V., Marcelino, S., Rivieccio, U.: Axiomatizing the logic of ordinary discourse. In: Proceeding of IPMU24 (2024)","DOI":"10.1007\/978-3-031-74000-8_32"},{"key":"4_CR21","unstructured":"Greati, V., Greco, G., Marcelino, S., Palmigiano, A., Rivieccio, U.: Generating proof systems for three-valued propositional logics. In: Egr\u00e9, P., Rossi, L. (eds.) Handbook of Three-Valued Logics. MIT Press (2024). https:\/\/arxiv.org\/abs\/2401.03274"},{"issue":"10","key":"4_CR22","doi-asserted-by":"publisher","first-page":"1138","DOI":"10.1017\/S0960129524000227","volume":"34","author":"V Greati","year":"2024","unstructured":"Greati, V., Marcelino, S., Marcos, J., Rivieccio, U.: Adding an implication to logics of perfect paradefinite algebras. Math. Struct. Comput. Sci. 34(10), 1138\u20131183 (2024). https:\/\/doi.org\/10.1017\/S0960129524000227","journal-title":"Math. Struct. Comput. Sci."},{"key":"4_CR23","doi-asserted-by":"crossref","unstructured":"Humberstone, L.: The Connectives. MIT Press (2011)","DOI":"10.7551\/mitpress\/9055.001.0001"},{"issue":"22","key":"4_CR24","doi-asserted-by":"publisher","first-page":"5373","DOI":"10.1007\/s11229-019-02142-8","volume":"198","author":"S Marcelino","year":"2021","unstructured":"Marcelino, S., Caleiro, C.: Axiomatizing non-deterministic many-valued generalized consequence relations. Synthese 198(22), 5373\u20135390 (2021)","journal-title":"Synthese"},{"key":"4_CR25","doi-asserted-by":"publisher","unstructured":"Pa\u0142asi\u0144ska, K.: Deductive systems and finite axiomatization properties (1994). https:\/\/doi.org\/10.31274\/rtd-180813-12680","DOI":"10.31274\/rtd-180813-12680"},{"issue":"1","key":"4_CR26","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/BF00258428","volume":"8","author":"G Priest","year":"1979","unstructured":"Priest, G.: The logic of paradox. J. Philos. Log. 8(1), 219\u2013241 (1979)","journal-title":"J. Philos. Log."},{"key":"4_CR27","doi-asserted-by":"publisher","unstructured":"Rivieccio, U.: The algebra of ordinary discourse. On the semantics of Cooper\u2019s logic. Arch. Math. Log. (2025). https:\/\/doi.org\/10.1007\/s00153-024-00961-2","DOI":"10.1007\/s00153-024-00961-2"},{"key":"4_CR28","doi-asserted-by":"crossref","unstructured":"Rivieccio, U., Mu\u00f1oz-P\u00e9rez, M.: Indicative conditionals: some algebraic considerations. In: WoLLIC 2025 (2025, accepted)","DOI":"10.1007\/978-3-031-99536-1_8"},{"key":"4_CR29","doi-asserted-by":"publisher","unstructured":"Shoesmith, D.J., Smiley, T.J.: Multiple-Conclusion Logic. Cambridge University Press, Cambridge (1978). https:\/\/doi.org\/10.1017\/CBO9780511565687","DOI":"10.1017\/CBO9780511565687"},{"key":"4_CR30","unstructured":"Wansing, H.: Connexive modal logic. In: Kracht, M., de\u00a0Rijke, M., Wansing, H., Zakharyaschev, M. (eds.) Advances in Modal Logic, pp. 367\u2013383. CSLI Publications (2005)"},{"key":"4_CR31","doi-asserted-by":"publisher","unstructured":"Wansing, H.: Constructive logic is connexive and contradictory. Log. Log. Philos. 1\u201327 (forthcoming). https:\/\/doi.org\/10.12775\/llp.2024.001","DOI":"10.12775\/llp.2024.001"},{"key":"4_CR32","doi-asserted-by":"publisher","unstructured":"W\u00f3jcicki, R.: Theory of Logical Calculi. Synthese Library, 1 edn. Springer, Dordrecht (1988). https:\/\/doi.org\/10.1007\/978-94-015-6942-2","DOI":"10.1007\/978-94-015-6942-2"}],"container-title":["Lecture Notes in Computer Science","Automated Reasoning with Analytic Tableaux and Related Methods"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-06085-3_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T10:45:23Z","timestamp":1758969923000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-06085-3_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,25]]},"ISBN":["9783032060846","9783032060853"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-06085-3_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,25]]},"assertion":[{"value":"25 September 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"TABLEAUX","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Automated Reasoning with Analytic Tableaux and Related Methods","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Reykjavik","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Iceland","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":"27 September 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29 September 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"34","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"tableaux2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/icetcs.github.io\/frocos-itp-tableaux25\/tableaux\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}