{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,15]],"date-time":"2025-11-15T09:55:55Z","timestamp":1763200555990,"version":"3.37.3"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,11,12]],"date-time":"2021-11-12T00:00:00Z","timestamp":1636675200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,12]],"date-time":"2021-11-12T00:00:00Z","timestamp":1636675200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["306530\/2019-8"],"award-info":[{"award-number":["306530\/2019-8"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stud Logica"],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s11225-021-09972-z","type":"journal-article","created":{"date-parts":[[2021,11,12]],"date-time":"2021-11-12T18:02:35Z","timestamp":1636740155000},"page":"601-642","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Two Decision Procedures for da Costa\u2019s $$C_n$$ Logics Based on Restricted Nmatrix Semantics"],"prefix":"10.1007","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1807-0520","authenticated-orcid":false,"given":"Marcelo E.","family":"Coniglio","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6539-398X","authenticated-orcid":false,"given":"Guilherme V.","family":"Toledo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,11,12]]},"reference":[{"key":"9972_CR1","unstructured":"Alves, E.\u00a0H., L\u00f3gica e inconsist\u00eancia: um estudo dos c\u00e1lculos$${\\bf C}_{n}$$, $$1\\le n<\\omega $$(Logic and inconsistency: a study of the calculi$${{\\bf C}}_{n}$$, $$1\\le n<\\omega $$, in Portuguese), Ph.D. thesis, Universidade de S\u00e3o Paulo, S\u00e3o Paulo, Brazil, 1976."},{"key":"9972_CR2","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/3-7643-7304-0_9","volume-title":"Logica Universalis","author":"A Avron","year":"2005","unstructured":"Avron, A., Non-deterministic matrices and modular semantics of rules, in J.\u00a0Y. Beziau, (ed.), Logica Universalis, Birkh\u00e4user, Basel, 2005, pp. 149\u2013167."},{"key":"9972_CR3","doi-asserted-by":"crossref","unstructured":"Avron, A., Non-deterministic semantics for paraconsistent C-systems, in L.\u00a0Godo, (ed.), Proceedings of the VIII European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2005), vol. 3571 of Lecture Notes in Computer Science, Springer, Berlin, 2005, pp. 625\u2013637.","DOI":"10.1007\/11518655_53"},{"issue":"2","key":"9972_CR4","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1016\/j.ijar.2006.06.011","volume":"45","author":"A Avron","year":"2007","unstructured":"Avron, A., Non-deterministic semantics for logics with a consistency operator, International Journal of Approximate Reasoning 45(2):271\u2013287, 2007.","journal-title":"International Journal of Approximate Reasoning"},{"issue":"7","key":"9972_CR5","doi-asserted-by":"publisher","first-page":"2167","DOI":"10.1007\/s00500-018-3272-0","volume":"23","author":"A Avron","year":"2019","unstructured":"Avron, A., Paraconsistency and the need for infinite semantics, Soft Computing 23(7):2167\u20132175, 2019.","journal-title":"Soft Computing"},{"key":"9972_CR6","unstructured":"Avron, A., O.\u00a0Arieli, and A.\u00a0Zamansky, Theory of Effective Propositional Paraconsistent Logics, vol.\u00a075 of Studies in Logic (Mathematical Logic and Foundations), College Publications, 2018."},{"issue":"4","key":"9972_CR7","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1093\/jigpal\/jzi030","volume":"13","author":"A Avron","year":"2005","unstructured":"Avron, A., and B.\u00a0Konikowska, Multi-valued calculi for logics based on non-determinism, Logic Journal of the IGPL 13(4):365\u2013387, 2005.","journal-title":"Logic Journal of the IGPL"},{"key":"9972_CR8","doi-asserted-by":"crossref","unstructured":"Avron, A., and I.\u00a0Lev, Canonical propositional Gentzen-type systems, in R.\u00a0Gor\u00e9, A.\u00a0Leitsch, and T.\u00a0Nipkow, (eds.), Proceedings of the First International Joint Conference on Automated Reasoning (IJCAR \u201901), vol. 2083 of Lecture Notes in Artificial Intelligence, Springer-Verlag, London, 2001, pp. 529\u2013544.","DOI":"10.1007\/3-540-45744-5_45"},{"issue":"3","key":"9972_CR9","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1093\/logcom\/exi001","volume":"15","author":"A Avron","year":"2005","unstructured":"Avron, A., and I.\u00a0Lev, Non-deterministic multi-valued structures, Journal of Logic and Computation 15(3):241\u2013261, 2005.","journal-title":"Journal of Logic and Computation"},{"issue":"4","key":"9972_CR10","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/s10817-013-9273-x","volume":"51","author":"M Baaz","year":"2013","unstructured":"Baaz, M., O.\u00a0Lahav, and A.\u00a0Zamansky, A finite-valued semantics for canonical labelled calculi, Journal of Automated Reasoning 51(4):401\u2013430, 2013.","journal-title":"Journal of Automated Reasoning"},{"key":"9972_CR11","doi-asserted-by":"crossref","unstructured":"Caleiro, C., and S.\u00a0Marcelino, Analytic calculi for monadic PNmatrices, in R.\u00a0Iemhoff, M.\u00a0Moortgat, and R.\u00a0de\u00a0Queiroz, (eds.), Logic, Language, Information, and Computation, vol. 11541 of Lecture Notes in Computer Science, Springer, 2019, pp. 84\u201398.","DOI":"10.1007\/978-3-662-59533-6_6"},{"issue":"2","key":"9972_CR12","doi-asserted-by":"publisher","first-page":"473","DOI":"10.2307\/2274395","volume":"52","author":"WA Carnielli","year":"1987","unstructured":"Carnielli, W.\u00a0A., Systematization of finite many-valued logics through the method of tableaux, The Journal of Symbolic Logic 52(2):473\u2013493, 1987.","journal-title":"The Journal of Symbolic Logic"},{"key":"9972_CR13","doi-asserted-by":"crossref","unstructured":"Carnielli, W.\u00a0A., and M.\u00a0E. Coniglio, Paraconsistent logic: Consistency, Contradiction and Negation, vol.\u00a040 of Logic, Epistemology, and the Unity of Science, Springer, 2016.","DOI":"10.1007\/978-3-319-33205-5"},{"key":"9972_CR14","doi-asserted-by":"crossref","unstructured":"Carnielli, W.\u00a0A., M.\u00a0E. Coniglio, and J.\u00a0Marcos, Logics of formal inconsistency, in D.\u00a0M. Gabbay, and F.\u00a0Guenthner, (eds.), Handbook of Philosophical Logic, vol.\u00a014, Springer, 2007, pp. 1\u201393.","DOI":"10.1007\/978-1-4020-6324-4_1"},{"key":"9972_CR15","doi-asserted-by":"crossref","unstructured":"Carnielli, W.\u00a0A., and J.\u00a0Marcos, A taxonomy of C-systems, in W.\u00a0A. Carnielli, M.\u00a0E. Coniglio, and I.\u00a0M. D\u2019Ottaviano, (eds.), Paraconsistency: The Logical Way to the Inconsistent, vol. 228 of Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, 2002, pp. 1\u201394.","DOI":"10.1201\/9780203910139.pt1"},{"key":"9972_CR16","doi-asserted-by":"crossref","unstructured":"Coniglio, M.\u00a0E., L.\u00a0Fari\u00f1as\u00a0del Cerro, and N.\u00a0M. Peron, Finite non-deterministic semantics for some modal systems, Journal of Applied Non-Classical Logic 25(1):20\u201345, 2015.","DOI":"10.1080\/11663081.2015.1011543"},{"key":"9972_CR17","doi-asserted-by":"crossref","unstructured":"Coniglio, M.\u00a0E., L.\u00a0Fari\u00f1as\u00a0del Cerro, and N.\u00a0M. Peron, Errata and addenda to Finite non-deterministic semantics for some modal systems, Journal of Applied Non-Classical Logic 26(4):336\u2013345, 2016.","DOI":"10.1080\/11663081.2017.1300436"},{"key":"9972_CR18","unstructured":"Coniglio, M.\u00a0E., L.\u00a0Fari\u00f1as\u00a0del Cerro, and N.\u00a0M. Peron, Tableau systems for some Ivlev-like (quantified) modal logics, to appear, 2021."},{"key":"9972_CR19","doi-asserted-by":"crossref","unstructured":"Coniglio, M.\u00a0E., and A.\u00a0Figallo\u00a0Orellano, A model-theoretic analysis of Fidel-structures for mbC, in C.\u00a0Baskent, and T.\u00a0Ferguson, (eds.), Graham Priest on Dialetheism and Paraconsistency, vol.\u00a014 of Outstanding Contributions to Logic, Springer, 2020, pp. 189\u2013216.","DOI":"10.1007\/978-3-030-25365-3_10"},{"key":"9972_CR20","doi-asserted-by":"crossref","unstructured":"Coniglio, M.\u00a0E., and G.\u00a0V. Toledo, A simple decision procedure for da Costa\u2019s $$C_n$$ logics by Restricted Nmatrix semantics, arXiv:2011.10151 [math.LO], 2020.","DOI":"10.1007\/s11225-021-09972-z"},{"key":"9972_CR21","unstructured":"da\u00a0Costa, N. C.\u00a0A., Sistemas formais inconsistentes (Inconsistent Formal Systems, in Portuguese), Universidade do Paran\u00e1, Curitiba, 1963 (republished by Editora UFPR, Brazil 1993)."},{"issue":"4","key":"9972_CR22","first-page":"621","volume":"18","author":"NCA da Costa","year":"1977","unstructured":"da\u00a0Costa, N. C.\u00a0A., and E.\u00a0H. Alves, A semantical analysis of the calculi $${\\mathbf{C}}_{n}$$, Notre Dame Journal of Formal Logic 18(4):621\u2013630, 1977.","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"9972_CR23","first-page":"201","volume":"24","author":"NCA da Costa","year":"1965","unstructured":"da\u00a0Costa, N. C.\u00a0A., and M.\u00a0Guillaume, N\u00e9gations compos\u00e9es et loi de Peirce dans les syst\u00e8mes $${\\bf C}_{n}$$, Portugaliae Mathematicae 24: 201\u2013210, 1965.","journal-title":"Portugaliae Mathematicae"},{"key":"9972_CR24","doi-asserted-by":"crossref","unstructured":"Dugundji, J., Note on a property of matrices for Lewis and Langford\u2019s calculi of propositions, The Journal of Symbolic Logic 5(4):150\u2013151, 1940.","DOI":"10.2307\/2268175"},{"key":"9972_CR25","first-page":"31","volume":"8","author":"MM Fidel","year":"1977","unstructured":"Fidel, M.\u00a0M., The decidability of the calculi $${C}_n$$, Reports on Mathematical Logic 8:31\u201340, 1977.","journal-title":"Reports on Mathematical Logic"},{"key":"9972_CR26","unstructured":"G\u00f6del, K., Zum intuitionistischen aussagenkalk\u00fcl, Anzeiger der AkademiederWissenschaften in Wien. Mathematisch-Naturwissenschaftliche Klasse 69:65\u201366, 1932 (translated as: On the intuitionistic propositional calculus, in: S. Feferman, J.W. Jr. Dawson, S.C. Kleene, G. Moore, R. Solovay, and J. Van Heijenoort, (eds.), Kurt G\u00f6del, Collected Works: Publications 1929\u20131936, Oxford University Press, New York, 1986, pp. 222\u2013225)."},{"key":"9972_CR27","doi-asserted-by":"crossref","unstructured":"Gr\u00e4tz, L., Analytic tableaux for non-deterministic semantics, in A.\u00a0Das, and S.\u00a0Negri, (eds.), Automated Reasoning with Analytic Tableaux and Related Methods, vol. 12842 of Lecture Notes in Artificial Intelligence, Springer International Publishing, 2021, pp. 38\u201355.","DOI":"10.1007\/978-3-030-86059-2_3"},{"key":"9972_CR28","unstructured":"Ivlev, Ju.\u00a0V., Tablitznoe postrojenie propozicionalnoj modalnoj logiki (Truth-tables for systems of propositional modal logic, in Russian), Vest. Mosk. Univ., Seria Filosofia, 6 1973."},{"issue":"3\/4","key":"9972_CR29","first-page":"114","volume":"17","author":"JuV Ivlev","year":"1988","unstructured":"Ivlev, Ju.\u00a0V., A semantics for modal calculi, Bulletin of the Section of Logic 17(3\/4):114\u2013121, 1988.","journal-title":"Bulletin of the Section of Logic"},{"key":"9972_CR30","doi-asserted-by":"crossref","unstructured":"Ja\u015bkowski, S., Rachunek zdan dla system\u00f3w dedukcyjnych sprzecznych, Studia Societatis Scientiarum Torunensis, 1(5):55\u201377, 1948 (translated as: Propositional calculus for contradictory deductive systems, Studia Logica 24:143\u2013157, 1969).","DOI":"10.1007\/BF02134311"},{"key":"9972_CR31","unstructured":"Ja\u015bkowski, S., O koniunkcji dyskusyjnej w rachunku zdan dla system\u00f3w dedukcyjnych sprzecznych, Studia Societatis Scientiarum Torunensis 8:171\u2013172, 1949 (translated as: On the discussive conjunction in the propositional calculus for inconsistent deductive systems, Logic and Logical Philosophy 7:57\u201359, 1999)."},{"issue":"1","key":"9972_CR32","doi-asserted-by":"publisher","first-page":"77","DOI":"10.2307\/2273259","volume":"46","author":"JT Kearns","year":"1981","unstructured":"Kearns, J.\u00a0T., Modal semantics without possible worlds, The Journal of Symbolic Logic 46(1):77\u201386, 1981.","journal-title":"The Journal of Symbolic Logic"},{"key":"9972_CR33","unstructured":"Lopari\u0107, A., and E.\u00a0H. Alves, The semantics of the systems $${\\bf C}_{n}$$ of da Costa, in A.\u00a0I. Arruda, N.\u00a0C.\u00a0A. da\u00a0Costa, and A.\u00a0M.\u00a0A. Sette, (eds.), Proceedings of the Third Brazilian Conference on Mathematical Logic, Sociedade Brasileira de L\u00f3gica, Recife, Brazil, 1980, pp. 161\u2013172."},{"issue":"5","key":"9972_CR34","first-page":"815","volume":"3","author":"H Omori","year":"2016","unstructured":"Omori, H., and D.\u00a0Skurt, More modal semantics without possible worlds, IfCoLog Journal of Logics and their Applications 3(5):815\u2013846, 2016.","journal-title":"IfCoLog Journal of Logics and their Applications"},{"key":"9972_CR35","unstructured":"Omori, H., and D.\u00a0Skurt, A semantics for a failed axiomatization of $$K$$, in N.\u00a0Olivietti, R.\u00a0Verbrugge, S.\u00a0Negri, and G.\u00a0Sandu, (eds.), Advances in Modal Logic, vol.\u00a013, College Publications, 2020, pp. 481\u2013501."},{"issue":"4","key":"9972_CR36","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1007\/s11787-020-00263-0","volume":"14","author":"P Pawlowski","year":"2020","unstructured":"Pawlowski, P, Tree-like proof systems for finitely-many valued non-deterministic consequence relations, Logica Universalis 14(4):407\u2013420, 2020.","journal-title":"Logic Universalis"},{"issue":"2","key":"9972_CR37","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1017\/S1755020317000363","volume":"11","author":"P Pawlowski","year":"2018","unstructured":"Pawlowski, P., and R.\u00a0Urbaniak, Many-valued logic of informal provability: a non-deterministic strategy, Review of Symbolic Logic 11(2):207\u2013223, 2018.","journal-title":"Review of Symbolic Logic"},{"key":"9972_CR38","first-page":"66","volume":"15A","author":"B Piochi","year":"1978","unstructured":"Piochi, B., Matrici adequate per calcoli generali predicativi, Bolletino della Unione Matematica Italiana 15A:66\u201376, 1978.","journal-title":"Bolletino della Unione Matematica Italiana"},{"issue":"1","key":"9972_CR39","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/BF01418757","volume":"42","author":"B Piochi","year":"1983","unstructured":"Piochi, B., Logical matrices and non-structural consequence operators, Studia Logica 42(1):33\u201342, 1983.","journal-title":"Studia Logica"},{"issue":"1","key":"9972_CR40","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2307\/2963674","volume":"27","author":"N Rescher","year":"1962","unstructured":"Rescher, N., Quasi-truth-functional systems of propositional logic, The Journal of Symbolic Logic 27(1):1\u201310, 1962.","journal-title":"The Journal of Symbolic Logic"},{"key":"9972_CR41","unstructured":"Smullyan, R.\u00a0M., First-Order Logic, Dover Publications, Mineola, N.Y. USA, 1995 (corrected republication of the Springer-Verlag, New York, 1968 edition)."},{"issue":"3","key":"9972_CR42","doi-asserted-by":"publisher","first-page":"269","DOI":"10.4064\/fm-68-3-269-279","volume":"68","author":"R W\u00f3jcicki","year":"1970","unstructured":"W\u00f3jcicki, R., Some remarks on the consequence operation in sentential logics, Fundamenta Mathematicae 68(3):269\u2013279, 1970.","journal-title":"Fundamenta Mathematicae"}],"container-title":["Studia Logica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11225-021-09972-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11225-021-09972-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11225-021-09972-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,28]],"date-time":"2022-05-28T17:09:51Z","timestamp":1653757791000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11225-021-09972-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,12]]},"references-count":42,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["9972"],"URL":"https:\/\/doi.org\/10.1007\/s11225-021-09972-z","relation":{},"ISSN":["0039-3215","1572-8730"],"issn-type":[{"type":"print","value":"0039-3215"},{"type":"electronic","value":"1572-8730"}],"subject":[],"published":{"date-parts":[[2021,11,12]]},"assertion":[{"value":"22 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 September 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 November 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}