{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T02:49:22Z","timestamp":1782182962750,"version":"3.54.5"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2015,2,27]],"date-time":"2015-02-27T00:00:00Z","timestamp":1424995200000},"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":["J Philos Logic"],"published-print":{"date-parts":[[2015,12]]},"DOI":"10.1007\/s10992-015-9358-6","type":"journal-article","created":{"date-parts":[[2015,2,26]],"date-time":"2015-02-26T04:15:24Z","timestamp":1424924124000},"page":"771-780","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Paraconsistent Logic"],"prefix":"10.1007","volume":"44","author":[{"given":"David","family":"Ripley","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2015,2,27]]},"reference":[{"issue":"4","key":"9358_CR1","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1007\/s10992-012-9241-7","volume":"42","author":"S Alxatib","year":"2013","unstructured":"Alxatib, S., Pagin, P., & Sauerland, U. (2013). Acceptable contradictions: Pragmatics or semantics? a reply to Cobreros et al. Journal of Philosophical Logic, 42(4), 619\u2013634.","journal-title":"Journal of Philosophical Logic"},{"issue":"3","key":"9358_CR2","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1111\/j.1468-0017.2011.01419.x","volume":"26","author":"S Alxatib","year":"2011","unstructured":"Alxatib, S., & Pelletier, J. (2011). The psychology of vagueness: Borderline cases and contradictions. Mind and Language, 26(3), 287\u2013326.","journal-title":"Mind and Language"},{"key":"9358_CR3","volume-title":"Entailment: The Logic of Relevance and Necessity, vol. 1","author":"AR Anderson","year":"1975","unstructured":"Anderson, A.R., & Belnap, N.D. (1975). Entailment: The Logic of Relevance and Necessity, vol. 1. Princeton: Princeton University Press."},{"key":"9358_CR4","unstructured":"Arruda, A.I. (1989). Aspects of the historical development of paraconsistent logic. In: [33], (pp. 99\u2013130)."},{"key":"9358_CR5","unstructured":"Batens, D. (1989). Dynamic dialectical logics. In: [33], (pp. 187\u2013217)."},{"key":"9358_CR6","doi-asserted-by":"crossref","first-page":"5","DOI":"10.12775\/LLP.2000.001","volume":"8","author":"D Batens","year":"2000","unstructured":"Batens, D. (2000). Towards the unification of inconsistency handling mechanisms. Logic and Logical Philosophy, 8, 5\u201331.","journal-title":"Logic and Logical Philosophy"},{"key":"9358_CR7","volume-title":"Possibilities and Paradox: An Introduction to Modal and Many-valued Logic","author":"J Beall","year":"2003","unstructured":"Beall, J., & van Fraassen, B.C. (2003). Possibilities and Paradox: An Introduction to Modal and Many-valued Logic. Oxford: Oxford University Press."},{"issue":"4","key":"9358_CR8","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/BF00284976","volume":"11","author":"ND Belnap","year":"1982","unstructured":"Belnap, N.D. (1982). Display logic. Journal of Philosophical Logic, 11(4), 375\u2013417.","journal-title":"Journal of Philosophical Logic"},{"key":"9358_CR9","volume-title":"Universal Logic","author":"RT Brady","year":"2006","unstructured":"Brady, R.T. (2006). Universal Logic. Stanford: CSLI Publications."},{"issue":"3","key":"9358_CR10","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1305\/ndjfl\/1022615617","volume":"40","author":"WA Carnielli","year":"1999","unstructured":"Carnielli, W.A., & Marcos, J. (1999). Limits for paraconsistent calculi. Notre Dame Journal of Formal Logic, 40(3), 375\u2013390.","journal-title":"Notre Dame Journal of Formal Logic"},{"issue":"5","key":"9358_CR11","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1111\/phc3.12030","volume":"8","author":"P Cobreros","year":"2013","unstructured":"Cobreros, P. (2013). Vagueness: Subvaluationism. Philosophy Compass, 8(5), 472\u2013485.","journal-title":"Philosophy Compass"},{"issue":"2","key":"9358_CR12","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s10992-010-9165-z","volume":"41","author":"P Cobreros","year":"2012","unstructured":"Cobreros, P., \u00c9gr\u00e9, P., Ripley, D., van Rooij, R. (2012). Tolerant, classical, strict. Journal of Philosophical Logic, 41(2), 347\u2013385.","journal-title":"Journal of Philosophical Logic"},{"key":"9358_CR13","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1305\/ndjfl\/1093891487","volume":"15","author":"N da Costa","year":"1974","unstructured":"da Costa, N. (1974). On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15, 497\u2013510.","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"9358_CR14","first-page":"128","volume-title":"The Continuum Companion to Philosophical Logic","author":"R Dietz","year":"2011","unstructured":"Dietz, R. (2011). The paradox of vagueness In Horsten, L., & Pettigrew, R. (Eds.), The Continuum Companion to Philosophical Logic, (pp. 128\u2013179). Great Britain: Continuum."},{"key":"9358_CR15","doi-asserted-by":"crossref","first-page":"331","DOI":"10.2307\/2214128","volume":"7","author":"JM Dunn","year":"1993","unstructured":"Dunn, J.M. (1993). Star and perp: Two treatments of negation. Philosophical Perspectives, 7, 331\u2013357.","journal-title":"Philosophical Perspectives"},{"key":"9358_CR16","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198531920.001.0001","volume-title":"Algebraic Methods in Philosophical Logic","author":"JM Dunn","year":"2001","unstructured":"Dunn, J.M., & Hardegree, G.M. (2001). Algebraic Methods in Philosophical Logic. Oxford: Oxford University Press."},{"issue":"5","key":"9358_CR17","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1093\/jigpal\/6.5.669","volume":"6","author":"R Gor\u00e9","year":"1998","unstructured":"Gor\u00e9, R. (1998). Gaggles, Gentzen, and Galois: How to display your favorite substructural logic. Logic Journal of the IGPL, 6(5), 669\u2013694.","journal-title":"Logic Journal of the IGPL"},{"key":"9358_CR18","volume-title":"The Connectives","author":"L Humberstone","year":"2012","unstructured":"Humberstone, L. (2012). The Connectives. Cambridge: MIT Press."},{"key":"9358_CR19","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1093\/mind\/106.424.641","volume":"106","author":"D Hyde","year":"1997","unstructured":"Hyde, D. (1997). From heaps and gaps to heaps of gluts. Mind, 106, 641\u2013660.","journal-title":"Mind"},{"key":"9358_CR20","volume-title":"Vagueness, Logic, and Ontology","author":"D Hyde","year":"2008","unstructured":"Hyde, D. (2008). Vagueness, Logic, and Ontology. Hampshire: Ashgate."},{"key":"9358_CR21","first-page":"49","volume":"24","author":"G Malinowski","year":"1990","unstructured":"Malinowski, G. (1990). Q-consequence operation. Reports on Mathematical Logic, 24, 49\u201359.","journal-title":"Reports on Mathematical Logic"},{"key":"9358_CR22","first-page":"407","volume":"15","author":"RK Meyer","year":"1972","unstructured":"Meyer, R.K., & Routley, R. (1972). Algebraic analysis of entailment I. Logique et Analyse, 15, 407\u2013428.","journal-title":"Logique et Analyse"},{"issue":"2","key":"9358_CR23","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/BF02120493","volume":"33","author":"RK Meyer","year":"1974","unstructured":"Meyer, R.K., & Routley, R. (1974). Classical relevant logics II. Studia Logica, 33(2), 183\u2013194.","journal-title":"Studia Logica"},{"key":"9358_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-8453-1","volume-title":"Inconsistent Mathematics","author":"C Mortensen","year":"1995","unstructured":"Mortensen, C. (1995). Inconsistent Mathematics. Dordrecht: Kluwer Academic Publishers."},{"key":"9358_CR25","unstructured":"O\u2019Connor, M. (2008). An introduction to smooth infinitesimal analysis. arXiv: 0805.3307 [math.GM]."},{"key":"9358_CR26","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/BF00258428","volume":"8","author":"G Priest","year":"1979","unstructured":"Priest, G. (1979). Logic of paradox. Journal of Philosophical Logic, 8, 219\u2013241.","journal-title":"Journal of Philosophical Logic"},{"key":"9358_CR27","volume-title":"Handbook of Philosophical Logic, Vol. 6","author":"G Priest","year":"2002","unstructured":"Priest, G. (2002). Paraconsistent logic. In Gabbay, D.M., & Guenthner, F. (Eds.), Handbook of Philosophical Logic, 2nd edn. Vol. 6. Dordrecht: Kluwer Academic Publishers. 2 edition.","edition":"2nd edn."},{"key":"9358_CR28","doi-asserted-by":"crossref","DOI":"10.1093\/0199262543.001.0001","volume-title":"Towards Non-Being: The Logic and Metaphysics of Intentionality","author":"G Priest","year":"2005","unstructured":"Priest, G. (2005). Towards Non-Being: The Logic and Metaphysics of Intentionality. Oxford: Oxford University Press."},{"key":"9358_CR29","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511801174","volume-title":"An Introduction to Non-Classical Logic: From If to Is","author":"G Priest","year":"2008","unstructured":"Priest, G. (2008). An Introduction to Non-Classical Logic: From If to Is, 2nd edn. Cambridge: Cambridge University Press.","edition":"2nd edn."},{"issue":"1","key":"9358_CR30","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1093\/jigpal\/jzs018","volume":"21","author":"G Priest","year":"2013","unstructured":"Priest, G. (2013). Mathematical pluralism. Logic Journal of the IGPL, 21(1), 4\u201313.","journal-title":"Logic Journal of the IGPL"},{"key":"9358_CR31","doi-asserted-by":"crossref","unstructured":"Priest, G., & Routley, R. (1989a). First historical introduction: A preliminary history of paraconsistent and dialetheic approaches. In: [33], (pp. 3\u201375).","DOI":"10.2307\/j.ctv2x8v8c7.4"},{"key":"9358_CR32","doi-asserted-by":"crossref","unstructured":"Priest, G., & Routley, R. (1989b). Systems of paraconsistent logic. In: [33], (pp. 151\u2013186).","DOI":"10.2307\/j.ctv2x8v8c7.8"},{"key":"9358_CR33","unstructured":"Priest, G., Routley, R., Norman, J. (Eds.) (1989). Paraconsistent Logic: Essays on the Inconsistent. Munich: Philosophia Verlag."},{"issue":"4","key":"9358_CR34","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1305\/ndjfl\/1039540771","volume":"38","author":"G Restall","year":"1997","unstructured":"Restall, G. (1997). Ways things can\u2019t be. Notre Dame Journal of Formal Logic, 38(4), 583\u2013596.","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"9358_CR35","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/978-94-015-9309-0_3","volume-title":"What is Negation?","author":"G Restall","year":"1999","unstructured":"Restall, G. (1999). Negation in relevant logics: How I stopped worrying and learned to love the Routley star In Gabbay, D., & Wansing, H. (Eds.), What is Negation? (pp. 53\u201376). Dordrecht: Kluwer Academic Publishers."},{"key":"9358_CR36","doi-asserted-by":"crossref","DOI":"10.4324\/9780203252642","volume-title":"An Introduction to Substructural Logics","author":"G Restall","year":"2000","unstructured":"Restall, G. (2000). An Introduction to Substructural Logics. London: Routledge."},{"key":"9358_CR37","doi-asserted-by":"crossref","unstructured":"Ripley, D., Nouwen, R., Rooij, R., Schmitz, H.-C., Sauerland, U. (2011a). Contradictions at the borders. Vagueness and Communication, (pp. 169\u2013188): Springer.","DOI":"10.1007\/978-3-642-18446-8_10"},{"key":"9358_CR38","unstructured":"Ripley, D. (2011b). Inconstancy and inconsistency In Cintula, P., Ferm\u00fcller, C., Godo, L., H\u00e1jek, P. (Eds.), Understanding Vagueness: Logical, Philosophical, and Linguistic Perspectives, (pp. 41\u201358): College Publications."},{"issue":"1","key":"9358_CR39","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s11229-012-0100-4","volume":"189","author":"D Ripley","year":"2012","unstructured":"Ripley, D. (2012). Structures and circumstances: Two ways to fine-grain propositions. Synthese, 189(1), 97\u2013118.","journal-title":"Synthese"},{"key":"9358_CR40","volume-title":"Relevant Logics and their Rivals 1","author":"R Routley","year":"1982","unstructured":"Routley, R., Meyer, R.K., Plumwood, V., Brady, R.T. (1982). Relevant Logics and their Rivals 1. Atascadero: Ridgeview."},{"issue":"4","key":"9358_CR41","doi-asserted-by":"crossref","first-page":"335","DOI":"10.2307\/2214309","volume":"6","author":"R Routley","year":"1972","unstructured":"Routley, R., & Routley, V. (1972). The semantics of first degree entailment. No\u00fbs, 6(4), 335\u2013359.","journal-title":"No\u00fbs"},{"key":"9358_CR42","first-page":"185","volume":"8","author":"R Routley","year":"1975","unstructured":"Routley, R., & Routley, V. (1975). The role of inconsistent and incomplete theories in the semantics of belief. Communication and Cognition, 8, 185\u2013235.","journal-title":"Communication and Cognition"},{"key":"9358_CR43","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511565687","volume-title":"Multiple-conclusion Logic","author":"DJ Shoesmith","year":"1978","unstructured":"Shoesmith, D.J., & Smiley, T.J. (1978). Multiple-conclusion Logic. Cambridge: Cambridge University Press."},{"key":"9358_CR44","unstructured":"Shramko, Y., & Wansing, H. (2012). Truth values. In Zalta, E.N. (Ed.), The Stanford Encyclopedia of Philosophy. Winter 2012 edition."},{"issue":"3\/4","key":"9358_CR45","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/BF00838045","volume":"39","author":"I Urbas","year":"1990","unstructured":"Urbas, I. (1990). Paraconsistency. Studies in Soviet Thought, 39(3\/4), 343\u2013354.","journal-title":"Studies in Soviet Thought"},{"issue":"4","key":"9358_CR46","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1305\/ndjfl\/1039540773","volume":"38","author":"A Varzi","year":"1997","unstructured":"Varzi, A. (1997). Inconsistency without contradiction. Notre Dame Journal of Formal Logic, 38(4), 621\u2013639.","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"9358_CR47","first-page":"279","volume-title":"Frontiers in Paraconsistent Logic","author":"A Varzi","year":"2000","unstructured":"Varzi, A. (2000). Supervaluationism and paraconsistency In Batens, D., Mortensen, C., Priest, G., Bendegem, J.-P.V. (Eds.), Frontiers in Paraconsistent Logic, (pp. 279\u2013297). Baldock: Research Studies Press."},{"issue":"1","key":"9358_CR48","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1093\/jigpal\/jzs025","volume":"21","author":"P Verd\u00e9e","year":"2013","unstructured":"Verd\u00e9e, P. (2013). Strong, universal, and provably non-trivial set theory by means of adaptive logic. Logic Journal of the IGPL, 21(1), 108\u2013125.","journal-title":"Logic Journal of the IGPL"},{"issue":"1","key":"9358_CR49","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1017\/S1755020309990281","volume":"3","author":"Z Weber","year":"2010","unstructured":"Weber, Z. (2010). Transfinite numbers in paraconsistent set theory. Review of Symbolic Logic, 3(1), 71\u201392.","journal-title":"Review of Symbolic Logic"},{"issue":"2","key":"9358_CR50","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1017\/S1755020312000019","volume":"5","author":"Z Weber","year":"2012","unstructured":"Weber, Z. (2012). Transfinite cardinals in paraconsistent set theory. Review of Symbolic Logic, 5(2), 269\u2013293.","journal-title":"Review of Symbolic Logic"},{"issue":"491","key":"9358_CR51","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1093\/mind\/fzu057","volume":"123","author":"Z Weber","year":"2014","unstructured":"Weber, Z., Ripley, D., Priest, G., Hyde, D., & Colyvan, M. (2014). Tolerating gluts: a reply to Beall. Mind, 123(491), 813\u2013828.","journal-title":"Mind"}],"container-title":["Journal of Philosophical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10992-015-9358-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10992-015-9358-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10992-015-9358-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,7]],"date-time":"2024-06-07T12:10:34Z","timestamp":1717762234000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10992-015-9358-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,27]]},"references-count":51,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2015,12]]}},"alternative-id":["9358"],"URL":"https:\/\/doi.org\/10.1007\/s10992-015-9358-6","relation":{},"ISSN":["0022-3611","1573-0433"],"issn-type":[{"value":"0022-3611","type":"print"},{"value":"1573-0433","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,27]]}}}