{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T10:45:16Z","timestamp":1774953916050,"version":"3.50.1"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T00:00:00Z","timestamp":1616630400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Questions concerning the proof-theoretic strength of classical versus nonclassical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of fixed-point semantics. It is known that nonclassical axiomatizations in four- or three-valued logics are substantially weaker than their classical counterparts. In this paper we consider the addition of a suitable conditional to First-Degree Entailment\u2014a logic recently studied by Hannes Leitgeb under the label <jats:bold>HYPE<\/jats:bold>. We show in particular that, by formulating the theory <jats:bold>PKF<\/jats:bold> over <jats:bold>HYPE<\/jats:bold>, one obtains a theory that is sound with respect to fixed-point models, while being proof-theoretically on a par with its classical counterpart <jats:bold>KF<\/jats:bold>. Moreover, we establish that also its schematic extension\u2014in the sense of Feferman\u2014is as strong as the schematic extension of <jats:bold>KF<\/jats:bold>, thus matching the strength of predicative analysis.<\/jats:p>","DOI":"10.1017\/s1755020321000137","type":"journal-article","created":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T03:09:55Z","timestamp":1616641795000},"page":"425-448","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":4,"title":["NONCLASSICAL TRUTH WITH CLASSICAL STRENGTH. A PROOF-THEORETIC ANALYSIS OF COMPOSITIONAL TRUTH OVER HYPE"],"prefix":"10.1017","volume":"16","author":[{"given":"MARTIN","family":"FISCHER","sequence":"first","affiliation":[]},{"given":"CARLO","family":"NICOLAI","sequence":"additional","affiliation":[]},{"given":"PABLO","family":"DOPICO","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,3,25]]},"reference":[{"key":"S1755020321000137_r3","doi-asserted-by":"publisher","DOI":"10.2307\/2274093"},{"key":"S1755020321000137_r27","first-page":"445","volume-title":"Logik-Texte","author":"Tarski","year":"1935"},{"key":"S1755020321000137_r19","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-018-9467-0"},{"key":"S1755020321000137_r11","volume-title":"Quantification in Nonclassical Logic","volume":"1","author":"Gabbay","year":"2009"},{"key":"S1755020321000137_r25","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/exab025"},{"key":"S1755020321000137_r4","doi-asserted-by":"publisher","DOI":"10.2307\/2274902"},{"key":"S1755020321000137_r7","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199230747.001.0001"},{"key":"S1755020321000137_r13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22156-3"},{"key":"S1755020321000137_r30","doi-asserted-by":"publisher","DOI":"10.1007\/BF00453022"},{"key":"S1755020321000137_r18","doi-asserted-by":"publisher","DOI":"10.2307\/2024634"},{"key":"S1755020321000137_r2","doi-asserted-by":"publisher","DOI":"10.2307\/2269764"},{"key":"S1755020321000137_r9","doi-asserted-by":"crossref","unstructured":"[9] Fischer, M. (2021) Sequent calculi for the propositional logic of hype. 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Published by Cambridge University Press on behalf of The Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http:\/\/creativecommons.org\/licenses\/by\/4.0), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}