{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:31:29Z","timestamp":1740123089101,"version":"3.37.3"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,2,3]],"date-time":"2021-02-03T00:00:00Z","timestamp":1612310400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,2,3]],"date-time":"2021-02-03T00:00:00Z","timestamp":1612310400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stud Logica"],"published-print":{"date-parts":[[2021,8]]},"DOI":"10.1007\/s11225-020-09926-x","type":"journal-article","created":{"date-parts":[[2021,2,3]],"date-time":"2021-02-03T12:06:07Z","timestamp":1612353967000},"page":"791-828","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Simple Logical Matrix and Sequent Calculus for Parry\u2019s Logic of Analytic Implication"],"prefix":"10.1007","volume":"109","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7324-0908","authenticated-orcid":false,"given":"Damian E.","family":"Szmuc","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,2,3]]},"reference":[{"issue":"2\u20133","key":"9926_CR1","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/0304-3975(88)90037-0","volume":"57","author":"A Avron","year":"1988","unstructured":"Avron, A., The semantics and proof theory of linear logic, Theoretical Computer Science 57(2-3):161\u2013184, 1988.","journal-title":"Theoretical Computer Science"},{"issue":"1","key":"9926_CR2","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/0890-5401(91)90023-U","volume":"92","author":"A Avron","year":"1991","unstructured":"Avron, A., Simple consequence relations, Information and Computation 92(1):105\u2013139, 1991.","journal-title":"Information and Computation"},{"key":"9926_CR3","first-page":"287","volume":"4","author":"D Bochvar","year":"1938","unstructured":"Bochvar, D., On a Three-Valued Calculus and its Application in the Analysis of the Paradoxes of the Extended Functional Calculus, Matematicheskii Sbornik 4:287\u2013308, 1938.","journal-title":"Matematicheskii Sbornik"},{"key":"9926_CR4","doi-asserted-by":"crossref","unstructured":"Bonzio, S., J. Gil-Ferez, F. Paoli, and L. Peruzzi, On Paraconsistent Weak Kleene, logic: Axiomatization and Algebraic Analysis, Studia Logica 105(2):253\u2013297, 2017.","DOI":"10.1007\/s11225-016-9689-5"},{"key":"9926_CR5","doi-asserted-by":"crossref","unstructured":"Bonzio, S., A. Loi, and L. Peruzzi, A Duality for Involutive Bisemilattices, Studia Logica 107(2): 423\u2013444, 2019.","DOI":"10.1007\/s11225-018-9801-0"},{"key":"9926_CR6","unstructured":"Bonzio, S., T. Moraschini, and M. Pra Baldi, Logics of left variable inclusion and P\u0142onka sums matrices, Reports on Mathematical Logic, forthcoming."},{"key":"9926_CR7","unstructured":"Bonzio, S., and M. Pra Baldi, Containment logics and P\u0142onka sums of matrices typescript."},{"key":"9926_CR8","unstructured":"Chemla, E., P. \u00c9gr\u00e9, and B. Spector, Characterizing logical consequence in many-valued logic, Journal of Logic and Computation 27(7):2193\u20132226, 2017."},{"key":"9926_CR9","first-page":"165","volume-title":"New Directions in Logic and the Philosophy of Science","author":"R Ciuni","year":"2016","unstructured":"Ciuni, R., and M. Carrara, Characterizing Logical Consequence in Paraconsistent Weak Kleene, in L. Felline, A. Ledda, F. Paoli, and E. Rossanese, (eds.), New Directions in Logic and the Philosophy of Science, College Publications, London, 2016, pp. 165\u2013176."},{"issue":"1","key":"9926_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/11663081.2018.1547514","volume":"29","author":"R Ciuni","year":"2019","unstructured":"Ciuni, R., and M. Carrara, Semantical analysis of weak Kleene logics, Journal of Applied Non-Classical Logics 29(1):1\u201336, 2019.","journal-title":"Journal of Applied Non-Classical Logics"},{"key":"9926_CR11","doi-asserted-by":"crossref","unstructured":"Ciuni, R., T. M. Ferguson, and D. Szmuc, Relevant Logics Obeying Component Homogeneity, Australasian Journal of Logic 15(2):301\u2013361, 2018.","DOI":"10.26686\/ajl.v15i2.4864"},{"key":"9926_CR12","doi-asserted-by":"crossref","unstructured":"Ciuni, R., T. M. Ferguson, and D. Szmuc, Logics based on Linear Orders of Contaminating Values, Journal of Logic and Computation 29(5):631\u2013663, 2019.","DOI":"10.1093\/logcom\/exz009"},{"key":"9926_CR13","doi-asserted-by":"crossref","unstructured":"Ciuni, R., T. M. Ferguson, and D. Szmuc, Modeling the Interaction of Computer Errors by Four-Valued Contaminating Logics, in R. Iemhoff, M. Moortgat, and R. de Queiroz, (eds.), Proceedings of the 26th International Workshop on Logic, Language, Information, and Computation (WoLLIC 2019), Springer, Berlin, 2019, pp. 119\u2013139.","DOI":"10.1007\/978-3-662-59533-6_8"},{"key":"9926_CR14","doi-asserted-by":"crossref","unstructured":"Coniglio, M., and M. I. Corbal\u00e1n, Sequent calculi for the classical fragment of Bochvar and Halld\u00e9n\u2019s Nonsense Logics, in Proceedings of the 7th Workshop on Logical and Semantic Frameworks with Applications (LSFA), 2012, pp. 125\u2013136.","DOI":"10.4204\/EPTCS.113.12"},{"key":"9926_CR15","doi-asserted-by":"crossref","unstructured":"Da R\u00e9, B., F. Pailos, and D. Szmuc, Theories of truth based on four-valued infectious logics. Logic Journal of the IGPL 28(5):712\u2013746, 2020.","DOI":"10.1093\/jigpal\/jzy057"},{"key":"9926_CR16","unstructured":"Epstein, R., The Semantic Foundations of Logic, Volume I: Propositional Logics, 2nd edition, Oxford University Press, New York, 1995."},{"issue":"4","key":"9926_CR17","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1080\/11663081.2014.980116","volume":"24","author":"TM Ferguson","year":"2014","unstructured":"Ferguson, T. M., A computational interpretation of conceptivism, Journal of Applied Non-Classical Logics 24(4):333\u2013367, 2014.","journal-title":"Journal of Applied Non-Classical Logics"},{"key":"9926_CR18","doi-asserted-by":"crossref","unstructured":"Ferguson, T. M., Logics of nonsense and Parry systems, Journal of Philosophical Logic 44(1):65\u201380, 2015.","DOI":"10.1007\/s10992-014-9321-y"},{"key":"9926_CR19","doi-asserted-by":"crossref","unstructured":"Ferguson, T. M., Faulty Belnap computers and subsystems of FDE, Journal of Logic and Computation 26(5):1617\u20131636, 2016.","DOI":"10.1093\/logcom\/exu048"},{"key":"9926_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-70821-8","volume-title":"Meaning and Proscription in Formal Logic: Variations on the Propositional Logic of William T. Parry","author":"TM Ferguson","year":"2017","unstructured":"Ferguson, T. M., Meaning and Proscription in Formal Logic: Variations on the Propositional Logic of William T. Parry, Springer, Dordrecht, 2017."},{"issue":"2","key":"9926_CR21","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1305\/ndjfl\/1093636609","volume":"27","author":"K Fine","year":"1986","unstructured":"Fine, K., Analytic implication, Notre Dame Journal of Formal Logic 27(2):169\u2013179, 1986.","journal-title":"Notre Dame Journal of Formal Logic"},{"issue":"2","key":"9926_CR22","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/s10992-015-9371-9","volume":"45","author":"K Fine","year":"2016","unstructured":"Fine, K., Angellic content, Journal of Philosophical Logic 45(2):199\u2013226, 2016.","journal-title":"Journal of Philosophical Logic"},{"key":"9926_CR23","volume-title":"Abstract Algebraic Logic","author":"JM Font","year":"2016","unstructured":"Font, J. M., Abstract Algebraic Logic, College Publications, London, 2016."},{"issue":"5","key":"9926_CR24","doi-asserted-by":"publisher","first-page":"971","DOI":"10.1007\/s11225-017-9719-y","volume":"105","author":"R French","year":"2017","unstructured":"French, R., A Simple Sequent Calculus for Angell\u2019s Logic of Analytic Containment, Studia Logica 105(5):971\u2013994, 2017.","journal-title":"Studia Logica"},{"key":"9926_CR25","first-page":"6","volume":"4","author":"K G\u00f6del","year":"1933","unstructured":"G\u00f6del, K., \u00dcber die Parryschen Axiome, Ergebnisse eines mathematischen Kolloquiums, 4:6, 1933.","journal-title":"Ergebnisse eines mathematischen Kolloquiums"},{"key":"9926_CR26","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/9055.001.0001","volume-title":"The Connectives","author":"L Humberstone","year":"2011","unstructured":"Humberstone, L., The Connectives, MIT Press, Cambridge, MA, 2011."},{"issue":"3","key":"9926_CR27","first-page":"123","volume":"1","author":"F Johnson","year":"1976","unstructured":"Johnson, F., A three-valued interpretation for a relevance logic, Relevance Logic Newsletter 1(3):123\u2013128, 1976.","journal-title":"Relevance Logic Newsletter"},{"issue":"4","key":"9926_CR28","first-page":"164","volume":"6","author":"F Johnson","year":"1977","unstructured":"Johnson, F., A natural deduction relevance logic, Bulletin of the Section of Logic 6(4):164\u2013168, 1977.","journal-title":"Bulletin of the Section of Logic"},{"key":"9926_CR29","unstructured":"Mares, E., Relevance Logic, in E. Zalta, (ed.), The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Metaphysics Research Lab, Stanford University, 2014."},{"key":"9926_CR30","doi-asserted-by":"crossref","unstructured":"Omori, H., and D. Szmuc, Conjunction and Disjunction in Infectious Logics, in A. Baltag, J. Seligman, and T. Yamada, (eds.), Proceedings of the 6th International Workshop on Logic, Rationality, and Interaction (LORI 2017), Springer, Berlin, 2017, pp. 268\u2013283.","DOI":"10.1007\/978-3-662-55665-8_19"},{"key":"9926_CR31","first-page":"153","volume-title":"Handbook of Paraconsistency","author":"F Paoli","year":"2007","unstructured":"Paoli, F., Tautological entailments and their rivals, in J.Y. B\u00e9ziau, W. Carnielli, and D. Gabbay, (eds.), Handbook of Paraconsistency, College Publications, London, 2007, pp. 153\u2013175."},{"key":"9926_CR32","doi-asserted-by":"crossref","unstructured":"Paoli, F., and M. Pra Baldi, Proof Theory of Paraconsistent Weak Kleene Logic, Studia Logica 4(108):779\u2013802, 2020.","DOI":"10.1007\/s11225-019-09876-z"},{"key":"9926_CR33","unstructured":"Paoli, F., and M. Pra Baldi, Extensions of Paraconsistent Weak Kleene Logic, Logic Journal of the IGPL, forthcoming."},{"key":"9926_CR34","unstructured":"Parry, W. T., Implication, Ph.D. thesis, Harvard University, 1932."},{"key":"9926_CR35","first-page":"5","volume":"4","author":"WT Parry","year":"1933","unstructured":"Parry, W. T., Ein axiomensystem f\u00fcr eine neue art von implikation (analytische implikation), Ergebnisse eines mathematischen Kolloquiums 4:5\u20136, 1933.","journal-title":"Ergebnisse eines mathematischen Kolloquiums"},{"key":"9926_CR36","unstructured":"Parry, W. T., The Logic of C.I. Lewis, in C. I. Lewis, and P. A. Schilpp, (eds.), The Philosophy of C. I. Lewis, Open Court, La Salle, Ill., 1968, pp. 115\u2013154."},{"issue":"1","key":"9926_CR37","first-page":"16","volume":"1","author":"WT Parry","year":"1976","unstructured":"Parry, W. T., Comparison of entailment theories, Relevance Logic Newsletter 1(1):16\u201326, 1976.","journal-title":"Relevance Logic Newsletter"},{"issue":"1","key":"9926_CR38","first-page":"11","volume":"1","author":"WT Parry","year":"1976","unstructured":"Parry, W. T., Entailment: analytic implication vs. the entailment of Anderson and Belnap, Relevance Logic Newsletter 1(1):11\u201315, 1976.","journal-title":"Relevance Logic Newsletter"},{"key":"9926_CR39","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/978-94-009-1005-8_7","volume-title":"Directions in Relevant Logic","author":"WT Parry","year":"1989","unstructured":"Parry, W. T., Analytic implication: its history, justification, and varieties, in J. Norman, and R. Sylvan, (eds.), Directions in Relevant Logic, Springer, Netherlands, 1989, pp. 101\u2013118."},{"issue":"1","key":"9926_CR40","doi-asserted-by":"publisher","first-page":"1","DOI":"10.26686\/ajl.v11i1.1830","volume":"11","author":"G Priest","year":"2014","unstructured":"Priest, G., Plurivalent Logics, Australasian Journal of Logic 11(1):1\u201313, 2014.","journal-title":"Australasian Journal of Logic"},{"key":"9926_CR41","volume-title":"Many-Valued Logic","author":"N Rescher","year":"1969","unstructured":"Rescher, N., Many-Valued Logic, McGraw-Hill, New York, 1969."},{"issue":"1","key":"9926_CR42","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1080\/00048402.2011.630010","volume":"91","author":"D Ripley","year":"2013","unstructured":"Ripley, D., Paradoxes and failures of cut, Australasian Journal of Philosophy 91(1):139\u2013164, 2013.","journal-title":"Australasian Journal of Philosophy"},{"key":"9926_CR43","first-page":"378","volume":"27","author":"T Smiley","year":"1962","unstructured":"Smiley, T., Analytic implication and 3-valued logic, Journal of Symbolic Logic 27:378, 1962.","journal-title":"Journal of Symbolic Logic"},{"issue":"4","key":"9926_CR44","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1080\/11663081.2017.1290488","volume":"26","author":"D Szmuc","year":"2017","unstructured":"Szmuc, D., Defining LFIs and LFUs in extensions of infectious logics, Journal of Applied Non-Classical Logics 26(4):286\u2013314, 2017.","journal-title":"Journal of Applied Non-Classical Logics"},{"issue":"2","key":"9926_CR45","first-page":"277","volume":"28","author":"D Szmuc","year":"2019","unstructured":"Szmuc, D., An Epistemic Interpretation of Paraconsistent Weak Kleene Logic, Logic and Logical Philosophy 28(2):277\u2013330, 2019.","journal-title":"Logic and Logical Philosophy"},{"issue":"2","key":"9926_CR46","doi-asserted-by":"publisher","first-page":"431","DOI":"10.26686\/ajl.v15i2.4867","volume":"15","author":"D Szmuc","year":"2018","unstructured":"Szmuc, D., and H. Omori, A Note on Goddard and Routley\u2019s Significance Logic, Australasian Journal of Logic 15(2):431\u2013448, 2018.","journal-title":"Australasian Journal of Logic"},{"key":"9926_CR47","unstructured":"Takeuti, G., Proof Theory, 2nd edition, Elsevier, Amsterdam, 1987."},{"key":"9926_CR48","doi-asserted-by":"crossref","unstructured":"Urquhart, A., Basic many-valued logic, in D. Gabbay and F. Guenthner, (eds.), Handbook of Philosophical Logic, Volume 2, 2nd edition, Springer, Berlin, 2001, pp. 249\u2013295.","DOI":"10.1007\/978-94-017-0452-6_4"}],"container-title":["Studia Logica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11225-020-09926-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11225-020-09926-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11225-020-09926-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,18]],"date-time":"2021-07-18T13:05:20Z","timestamp":1626613520000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11225-020-09926-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,3]]},"references-count":48,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["9926"],"URL":"https:\/\/doi.org\/10.1007\/s11225-020-09926-x","relation":{},"ISSN":["0039-3215","1572-8730"],"issn-type":[{"type":"print","value":"0039-3215"},{"type":"electronic","value":"1572-8730"}],"subject":[],"published":{"date-parts":[[2021,2,3]]},"assertion":[{"value":"3 January 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 February 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}