{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T02:56:29Z","timestamp":1772938589115,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T00:00:00Z","timestamp":1767571200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T00:00:00Z","timestamp":1767571200000},"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":["J Philos Logic"],"published-print":{"date-parts":[[2026,2]]},"DOI":"10.1007\/s10992-025-09827-1","type":"journal-article","created":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T12:42:53Z","timestamp":1767616973000},"page":"167-198","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Simple Paraconsistent Logic without Addition"],"prefix":"10.1007","volume":"55","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7211-0044","authenticated-orcid":false,"given":"Philipp","family":"Mayr","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,1,5]]},"reference":[{"issue":"5","key":"9827_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3765\/sp.15.5","volume":"15","author":"M Aloni","year":"2022","unstructured":"Aloni, M. (2022). Logic and conversation: The case of free choice. Semantics and Pragmatics, 15(5), 1\u201360. https:\/\/doi.org\/10.3765\/sp.15.5","journal-title":"Semantics and Pragmatics"},{"issue":"1\/2","key":"9827_CR2","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/BF00818100","volume":"13","author":"AR Anderson","year":"1962","unstructured":"Anderson, A. R., & Belnap, N. D. (1962). Tautological entailments. Philosophical Studies, 13(1\/2), 9\u201324.","journal-title":"Philosophical Studies"},{"key":"9827_CR3","unstructured":"Anderson, A. R., & Belnap, N. D. (1975). Entailment: The logic of relevance and necessity (Vol.\u00a01). Princeton University Press."},{"key":"9827_CR4","doi-asserted-by":"publisher","unstructured":"Angell, R. B. (1989). Deducibility, entailment and analytic containment. In J. Norman & R. Sylvan (Eds.), Directions in relevant logic (pp.\u00a0119\u2013143). Kluwer. https:\/\/doi.org\/10.1007\/978-94-009-1005-8_8","DOI":"10.1007\/978-94-009-1005-8_8"},{"issue":"2","key":"9827_CR5","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1305\/ndjfl\/1093635414","volume":"31","author":"A Avron","year":"1990","unstructured":"Avron, A. (1990). Relevance and paraconsistency\u2013a new approach part II: The formal systems. Notre Dame Journal of Formal Logic, 31(2), 169\u2013202.","journal-title":"Notre Dame Journal of Formal Logic"},{"issue":"173\/75","key":"9827_CR6","first-page":"45","volume":"44","author":"D Batens","year":"2001","unstructured":"Batens, D. (2001). A general characterization of adaptive logics. Logique et Analyse, 44(173\/75), 45\u201368.","journal-title":"Logique et Analyse"},{"issue":"3","key":"9827_CR7","doi-asserted-by":"publisher","first-page":"143","DOI":"10.5840\/jphil2013110336","volume":"110","author":"JC Beall","year":"2013","unstructured":"Beall, J. C., & Murzi, J. (2013). Two flavors of Curry\u2019s paradox. Journal of Philosophy, 110(3), 143\u2013165.","journal-title":"Journal of Philosophy"},{"issue":"4","key":"9827_CR8","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1007\/s10670-015-9764-8","volume":"81","author":"D Bonnay","year":"2016","unstructured":"Bonnay, D., & Westerst\u00e5hl, D. (2016). Compositionality solves Carnap\u2019s problem. Erkenntnis, 81(4), 721\u2013739.","journal-title":"Erkenntnis"},{"key":"9827_CR9","volume-title":"Making it explicit","author":"RB Brandom","year":"1994","unstructured":"Brandom, R. B. (1994). Making it explicit. Harvard University Press."},{"key":"9827_CR10","volume-title":"Formalization of logic","author":"R Carnap","year":"1943","unstructured":"Carnap, R. (1943). Formalization of logic. Harvard University Press."},{"key":"9827_CR11","volume-title":"The logical basis of metaphysics","author":"M Dummett","year":"1991","unstructured":"Dummett, M. (1991). The logical basis of metaphysics. Harvard University Press."},{"issue":"2","key":"9827_CR12","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1305\/ndjfl\/1093894715","volume":"13","author":"JM Dunn","year":"1972","unstructured":"Dunn, J. M. (1972). A modification of Parry\u2019s analytic implication. Notre Dame Journal of Formal Logic, 13(2), 195\u2013205.","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"9827_CR13","doi-asserted-by":"crossref","unstructured":"Dunn, J. M., & Restall, G. (2002). Relevance logic. In: Handbook of philosophical logic (pp.\u00a01\u2013128). Springer.","DOI":"10.1007\/978-94-017-0460-1_1"},{"key":"9827_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-70821-8","volume-title":"Meaning and proscription in formal logic","author":"TM Ferguson","year":"2017","unstructured":"Ferguson, T. M. (2017). Meaning and proscription in formal logic. Springer."},{"issue":"2","key":"9827_CR15","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/s10992-015-9371-9","volume":"45","author":"K Fine","year":"2016","unstructured":"Fine, K. (2016). Angellic content. Journal of Philosophical Logic, 45(2), 199\u2013226.","journal-title":"Journal of Philosophical Logic"},{"issue":"2","key":"9827_CR16","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1002\/tht3.482","volume":"10","author":"C Gauker","year":"2021","unstructured":"Gauker, C. (2021). A strictly stronger relative Must. Thought, 10(2), 82\u201389.","journal-title":"Thought"},{"key":"9827_CR17","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1007\/BF01201353","volume":"35","author":"G Gentzen","year":"1935","unstructured":"Gentzen, G. (1935). Untersuchungen \u00fcber das logische Schlie\u00dfen. I. Mathematische Zeitschrift, 35, 176\u2013210.","journal-title":"I. Mathematische Zeitschrift"},{"key":"9827_CR18","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1007\/s10988-020-09295-7","volume":"44","author":"P Hawke","year":"2021","unstructured":"Hawke, P., & Steinert-Threlkeld, S. (2021). Semantic expressivism for epistemic modals. Linguistics and Philosophy, 44, 475\u2013511.","journal-title":"Linguistics and Philosophy"},{"issue":"3","key":"9827_CR19","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1080\/0020174X.2020.1762728","volume":"65","author":"ST Hewitt","year":"2022","unstructured":"Hewitt, S. T. (2022). Need anything follow from a contradiction? Inquiry, 65(3), 278\u2013297.","journal-title":"Inquiry"},{"key":"9827_CR20","doi-asserted-by":"publisher","first-page":"831","DOI":"10.1007\/s10992-024-09746-7","volume":"53","author":"W Holliday","year":"2024","unstructured":"Holliday, W., & Mandelkern, M. (2024). The orthologic of epistemic modals. Journal of Philosophical Logic, 53, 831\u2013907.","journal-title":"Journal of Philosophical Logic"},{"key":"9827_CR21","volume-title":"Reasoning with attitude","author":"L Incurvati","year":"2023","unstructured":"Incurvati, L., & Schl\u00f6der, J. J. (2023). Reasoning with attitude. Oxford University Press."},{"key":"9827_CR22","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/BF02134311","volume":"24","author":"S Ja\u015bkowski","year":"1969","unstructured":"Ja\u015bkowski, S. (1969). Propositional calculus for contradictory deductive systems (communicated 1948). Studia Logica, 24, 143\u2013160.","journal-title":"Studia Logica"},{"key":"9827_CR23","volume-title":"The development of logic","author":"WC Kneale","year":"1962","unstructured":"Kneale, W. C., & Kneale, M. (1962). The development of logic. Oxford University Press."},{"key":"9827_CR24","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780192870049.001.0001","volume-title":"Bounded meaning: The dynamics of interpretation","author":"M Mandelkern","year":"2024","unstructured":"Mandelkern, M. (2024). Bounded meaning: The dynamics of interpretation. Oxford: Oxford University Press."},{"issue":"9","key":"9827_CR25","doi-asserted-by":"publisher","first-page":"462","DOI":"10.2307\/2026276","volume":"82","author":"V McGee","year":"1985","unstructured":"McGee, V. (1985). A counterexample to modus ponens. Journal of Philosophy, 82(9), 462\u2013471.","journal-title":"Journal of Philosophy"},{"issue":"2","key":"9827_CR26","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/s10670-018-0032-6","volume":"85","author":"J Murzi","year":"2020","unstructured":"Murzi, J. (2020). Classical harmony and separability. Erkenntnis, 85(2), 391\u2013415.","journal-title":"Erkenntnis"},{"issue":"1","key":"9827_CR27","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1080\/00048402.2019.1640323","volume":"98","author":"J Murzi","year":"2021","unstructured":"Murzi, J., & Rossi, L. (2021). Generalized revenge. Australasian Journal of Philosophy, 98(1), 153\u2013177.","journal-title":"Australasian Journal of Philosophy"},{"key":"9827_CR28","doi-asserted-by":"crossref","unstructured":"Murzi, J., & Steinberger, F. (2017). Inferentialism. In: A companion to the philosophy of language (pp.\u00a0197\u2013224). Wiley.","DOI":"10.1002\/9781118972090.ch9"},{"issue":"10","key":"9827_CR29","doi-asserted-by":"publisher","first-page":"3391","DOI":"10.1007\/s11098-021-01606-3","volume":"178","author":"J Murzi","year":"2021","unstructured":"Murzi, J., & Topey, B. (2021). Categoricity by convention. Philosophical Studies, 178(10), 3391\u20133420.","journal-title":"Philosophical Studies"},{"issue":"5","key":"9827_CR30","doi-asserted-by":"publisher","first-page":"1355","DOI":"10.1007\/s10992-023-09709-4","volume":"52","author":"S Niki","year":"2023","unstructured":"Niki, S., & Wansing, H. (2023). On the provable contradictions of the connexive logics C and C3. Journal of Philosophical Logic, 52(5), 1355\u20131383.","journal-title":"Journal of Philosophical Logic"},{"key":"9827_CR31","unstructured":"Parry, W. T. (1933). Ein Axiomensystem f\u00fcr eine neue Art von Implikation (analytische Implikation). Ergebnisse eines mathematischen Kolloquiums, 4(5\u20136)."},{"key":"9827_CR32","volume-title":"From explosion to implosion: A new justification for the ex falso quodlibet rule","author":"I Pezlar","year":"2024","unstructured":"Pezlar, I. (2024). From explosion to implosion: A new justification for the ex falso quodlibet rule. Erkenntnis: Advance online publication."},{"key":"9827_CR33","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1093\/0195148770.003.0022","volume-title":"The Oxford handbook of philosophy of mathematics and logic","author":"D Prawitz","year":"2005","unstructured":"Prawitz, D. (2005). Logical consequence: A constructivist view. In S. Shapiro (Ed.), The Oxford handbook of philosophy of mathematics and logic (pp. 671\u2013695). Oxford University Press."},{"issue":"1","key":"9827_CR34","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/BF00258428","volume":"8","author":"G Priest","year":"1979","unstructured":"Priest, G. (1979). The logic of paradox. Journal of Philosophical Logic, 8(1), 219\u2013241.","journal-title":"Journal of Philosophical Logic"},{"issue":"436","key":"9827_CR35","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1093\/mind\/109.436.781","volume":"109","author":"I Rumfitt","year":"2000","unstructured":"Rumfitt, I. (2000). Yes and No. Mind, 109(436), 781\u2013823.","journal-title":"Mind"},{"key":"9827_CR36","volume-title":"A companion to the philosophy of language","author":"I Rumfitt","year":"2017","unstructured":"Rumfitt, I. (2017). Against harmony. In B. Hale, C. Wright, & A. Miller (Eds.), A companion to the philosophy of language. Wiley."},{"issue":"1\u20133","key":"9827_CR37","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/BF00388295","volume":"35","author":"G Schurz","year":"1991","unstructured":"Schurz, G. (1991). Relevant deduction: From solving paradoxes towards a general theory. Erkenntnis, 35(1\u20133), 391\u2013437.","journal-title":"Erkenntnis"},{"issue":"1","key":"9827_CR38","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1093\/analys\/56.1.1","volume":"56","author":"T Smiley","year":"1996","unstructured":"Smiley, T. (1996). Rejection. Analysis, 56(1), 1\u20139.","journal-title":"Rejection. Analysis"},{"key":"9827_CR39","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/978-94-015-9309-0_10","volume-title":"What is negation?","author":"N Tennant","year":"1999","unstructured":"Tennant, N. (1999). Negation, absurdity and contrariety. In D. M. Gabbay & H. Wansing (Eds.), What is negation? (pp. 199\u2013222). Springer."},{"key":"9827_CR40","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198777892.001.0001","volume-title":"Core logic","author":"N Tennant","year":"2017","unstructured":"Tennant, N. (2017). Core logic. Oxford University Press."},{"key":"9827_CR41","volume-title":"The Stanford encyclopedia of philosophy","author":"H Wansing","year":"2023","unstructured":"Wansing, H. (2023). Connexive logic. In E. N. Zalta & U. Nodelman (Eds.), The Stanford encyclopedia of philosophy. Stanford University."},{"issue":"1","key":"9827_CR42","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/s10670-022-00528-8","volume":"89","author":"H Wansing","year":"2024","unstructured":"Wansing, H. (2024). One heresy and one orthodoxy: On dialetheism, dimathematism, and the non-normativity of logic. Erkenntnis, 89(1), 181\u2013205.","journal-title":"Erkenntnis"},{"key":"9827_CR43","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780190086152.001.0001","volume-title":"Shadows of syntax","author":"J Warren","year":"2020","unstructured":"Warren, J. (2020). Shadows of syntax. Oxford University Press."},{"issue":"1","key":"9827_CR44","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1111\/phis.12131","volume":"28","author":"T Williamson","year":"2018","unstructured":"Williamson, T. (2018). Alternative logics and applied mathematics. Philosophical Issues, 28(1), 399\u2013424.","journal-title":"Philosophical Issues"},{"key":"9827_CR45","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198860662.001.0001","volume-title":"Suppose and tell: The semantics and heuristics of conditionals","author":"T Williamson","year":"2020","unstructured":"Williamson, T. (2020). Suppose and tell: The semantics and heuristics of conditionals. Oxford: Oxford University Press."},{"key":"9827_CR46","volume-title":"Tractatus logico-philosophicus","author":"L Wittgenstein","year":"1922","unstructured":"Wittgenstein, L. (1922). Tractatus logico-philosophicus. London: Kegan Paul."},{"key":"9827_CR47","doi-asserted-by":"publisher","first-page":"983","DOI":"10.1093\/mind\/fzm983","volume":"116","author":"S Yalcin","year":"2007","unstructured":"Yalcin, S. (2007). Epistemic modals. Mind, 116, 983\u20131026.","journal-title":"Mind"},{"issue":"6","key":"9827_CR48","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1007\/s10992-012-9228-4","volume":"41","author":"S Yalcin","year":"2012","unstructured":"Yalcin, S. (2012). A counterexample to modus tollens. Journal of Philosophical Logic, 41(6), 1001\u20131024.","journal-title":"Journal of Philosophical Logic"}],"container-title":["Journal of Philosophical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10992-025-09827-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10992-025-09827-1","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10992-025-09827-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T09:02:57Z","timestamp":1772874177000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10992-025-09827-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,5]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["9827"],"URL":"https:\/\/doi.org\/10.1007\/s10992-025-09827-1","relation":{},"ISSN":["0022-3611","1573-0433"],"issn-type":[{"value":"0022-3611","type":"print"},{"value":"1573-0433","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,5]]},"assertion":[{"value":"28 May 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 December 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 January 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}},{"value":"There are no competing interests to report.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}