{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T00:21:28Z","timestamp":1773447688763,"version":"3.50.1"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2011,3,29]],"date-time":"2011-03-29T00:00:00Z","timestamp":1301356800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Synthese"],"published-print":{"date-parts":[[2012,8]]},"DOI":"10.1007\/s11229-011-9910-z","type":"journal-article","created":{"date-parts":[[2011,3,28]],"date-time":"2011-03-28T08:45:53Z","timestamp":1301301953000},"page":"925-942","source":"Crossref","is-referenced-by-count":30,"title":["The categorical and the hypothetical: a critique of some fundamental assumptions of standard semantics"],"prefix":"10.1007","volume":"187","author":[{"given":"Peter","family":"Schroeder-Heister","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,3,29]]},"reference":[{"key":"9910_CR1","doi-asserted-by":"crossref","unstructured":"Brotherston, J., & Simpson, A. (2007). Complete sequent calculi for induction and infinite descent. In Proceedings of the 22nd annual IEEE symposium on logic in computer science (LICS), (pp. 51\u201362). Los Alamitos: IEEE Press.","DOI":"10.1109\/LICS.2007.16"},{"key":"9910_CR2","unstructured":"Dummett, M. (1978). The justification of deduction (1973). In Truth and Other Enigmas. London: Duckworth."},{"key":"9910_CR3","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/S0304-3975(06)80007-1","volume":"87","author":"L. Halln\u00e4s","year":"1991","unstructured":"Halln\u00e4s L. (1991) Partial inductive definitions. Theoretical Computer Science 87: 115\u2013142","journal-title":"Theoretical Computer Science"},{"key":"9910_CR4","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1007\/s11229-004-6291-6","volume":"148","author":"L. Halln\u00e4s","year":"2006","unstructured":"Halln\u00e4s L. (2006) On the proof-theoretic foundation of general definition theory. Synthese 148: 589\u2013602","journal-title":"Synthese"},{"key":"9910_CR5","doi-asserted-by":"crossref","unstructured":"Halln\u00e4s, L., & Schroeder-Heister, P. (1990\/91). A proof-theoretic approach to logic programming: I. Clauses as rules. II. Programs as definitions. Journal of Logic and Computation, 1, 261\u2013283, 635\u2013660.","DOI":"10.1093\/logcom\/1.2.261"},{"key":"9910_CR6","unstructured":"Halln\u00e4s, L., & Schroeder-Heister, P. (2012). A survey of definitional reflection (in preparation)."},{"key":"9910_CR7","unstructured":"Kreuger, P. (1994). Axioms in definitional calculi. In R. Dychhoff (Ed.), Extensions of logic programming. 4th international workshop, ELP\u201993 (St. Andrews,U.K., March\/April 1993). Proceedings (Lecture Notes in Computer Science) (Vol. 798, pp. 196\u2013205). Berlin: Springer."},{"key":"9910_CR8","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1007\/BF01162411","volume":"53","author":"P. Lorenzen","year":"1950","unstructured":"Lorenzen P. (1950) Konstruktive Begr\u00fcndung der Mathematik. Mathematische Zeitschrift 53: 162\u2013202","journal-title":"Mathematische Zeitschrift"},{"key":"9910_CR9","doi-asserted-by":"crossref","unstructured":"Lorenzen, P. (1955). Einf\u00fchrung in die operative Logik und Mathematik (2nd Edn. 1969). Berlin: Springer.","DOI":"10.1007\/978-3-662-01539-1"},{"key":"9910_CR10","doi-asserted-by":"crossref","unstructured":"Orevkov, V. P. (1982). Lower bounds for increasing complexity of derivations after cut elimination (Transl., russ. orig. 1979). Journal of Soviet Mathematics, 20, 2337\u20132350.","DOI":"10.1007\/BF01629444"},{"key":"9910_CR11","doi-asserted-by":"crossref","first-page":"163","DOI":"10.2307\/2370324","volume":"43","author":"E. L. Post","year":"1921","unstructured":"Post E. L. (1921) Introduction to a general theory of elementary propositions. American Journal of Mathematics 43: 163\u2013185","journal-title":"American Journal of Mathematics"},{"key":"9910_CR12","doi-asserted-by":"crossref","first-page":"197","DOI":"10.2307\/2371809","volume":"65","author":"E. L. Post","year":"1943","unstructured":"Post E. L. (1943) Formal reductions of the general combinatorial decision problem. American Journal of Mathematics 65: 197\u2013215","journal-title":"American Journal of Mathematics"},{"key":"9910_CR13","unstructured":"Prawitz, D. (1965). Natural Deduction: A Proof-Theoretical Study. Almqvist & Wiksell: Stockholm (Reprinted Mineola NY: Dover Publ., 2006)."},{"key":"9910_CR14","doi-asserted-by":"crossref","unstructured":"Prawitz, D. (1973). Towards a foundation of a general proof theory. In P. Suppes et\u00a0al. (Eds.), Logic, methodology and philosophy of science IV (pp. 225\u2013250). Amsterdam: North-Holland","DOI":"10.1016\/S0049-237X(09)70361-1"},{"key":"9910_CR15","doi-asserted-by":"crossref","unstructured":"Prawitz, D. (1979). Proofs and the meaning and completeness of the logical constants. In J. Hintikka et\u00a0al. (Eds.), Essays on mathematical and philosophical logic (pp. 25\u201340). Dordrecht: Kluwer","DOI":"10.1007\/978-94-009-9825-4_2"},{"key":"9910_CR16","doi-asserted-by":"crossref","first-page":"1284","DOI":"10.2307\/2274279","volume":"49","author":"P. Schroeder-Heister","year":"1984","unstructured":"Schroeder-Heister P. (1984) A natural extension of natural deduction. Journal of Symbolic Logic 49: 1284\u20131300","journal-title":"Journal of Symbolic Logic"},{"key":"9910_CR17","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1017\/CBO9780511569807.016","volume-title":"Logical frameworks","author":"P. Schroeder-Heister","year":"1991","unstructured":"Schroeder-Heister P. (1991) Structural frameworks, substructural logics, and the role of elimination inferences. In: Huet G., Plotkin G. (eds) Logical frameworks. Cambridge University Press, New York, pp 385\u2013403"},{"key":"9910_CR18","unstructured":"Schroeder-Heister, P. (1992). Cut elimination in logics with definitional reflection. In D. Pearce & H. Wansing (Eds.), Nonclassical logics and information processing: International workshop, Berlin, November 1990, Proceedings (Lecture Notes in Computer Science) (Vol. 619, pp. 146\u2013171). Berlin: Springer."},{"key":"9910_CR19","unstructured":"Schroeder-Heister, P. (2004). On the notion of assumption in logical systems. In R. Bluhm & C. Nimtz (Eds.), Selected papers contributed to the sections of GAP5, fifth international congress of the Society for Analytical Philosophy, Bielefeld, 22\u201326 September 2003 (pp. 27\u201348). Mentis: Paderborn http:\/\/www.gap5.de\/proceedings ."},{"key":"9910_CR20","unstructured":"Schroeder-Heister, P. (2008). Proof-theoretic versus model-theoretic consequence. In M. Peli\u0161 (Ed.), The Logica Yearbook 2007 (pp. 187\u2013200). Filosofia: Prague."},{"key":"9910_CR21","volume-title":"The Logica Yearbook 2008","author":"P. Schroeder-Heister","year":"2009","unstructured":"Schroeder-Heister P. (2009) Sequent calculi and bidirectional natural deduction: On the proper basis of proof-theoretic semantics. In: Peli\u0161 M. (eds) The Logica Yearbook 2008. College Publications, London"},{"key":"9910_CR22","unstructured":"Schroeder-Heister, P. (2011a). Generalized elimination inferences, higher-level rules, and the implications-as-rules interpretation of the sequent calculus. In E. H. Haeusler, L. C. Pereira, & V. de Paiva (Eds.), Advances in natural deduction."},{"key":"9910_CR23","doi-asserted-by":"crossref","unstructured":"Schroeder-Heister, P. (2011b). Implications-as-rules vs. implications-as-links: An alternative implication-left schema for the sequent calculus. Journal of Philosophical Logic, 40 95\u2013101.","DOI":"10.1007\/s10992-010-9149-z"},{"key":"9910_CR24","unstructured":"Schroeder-Heister, P. (2011c). Proof-theoretic semantics. In Ed. Zalta (Ed.), Stanford Encyclopedia of Philosophy. Stanford: Stanford University. http:\/\/plato.stanford.edu ."},{"key":"9910_CR25","doi-asserted-by":"crossref","unstructured":"Smullyan, R. (1961). Theory of formal systems. Annals of mathematics studies 47. Princeton: Princeton University Press.","DOI":"10.1515\/9781400882007"},{"key":"9910_CR26","first-page":"104","volume":"75","author":"R. Statman","year":"1979","unstructured":"Statman R. (1979) Lower bounds on Herbrand\u2019s theorem. Proceedings of the American Mathematical Society 75: 104\u2013107","journal-title":"Proceedings of the American Mathematical Society"}],"container-title":["Synthese"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11229-011-9910-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11229-011-9910-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11229-011-9910-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,17]],"date-time":"2020-06-17T17:15:49Z","timestamp":1592414149000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11229-011-9910-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,29]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["9910"],"URL":"https:\/\/doi.org\/10.1007\/s11229-011-9910-z","relation":{},"ISSN":["0039-7857","1573-0964"],"issn-type":[{"value":"0039-7857","type":"print"},{"value":"1573-0964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3,29]]}}}