{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T21:04:10Z","timestamp":1771448650889,"version":"3.50.1"},"reference-count":36,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T00:00:00Z","timestamp":1769472000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"National Office for Philosophy and Social Sciences of China","award":["23&ZD240"],"award-info":[{"award-number":["23&ZD240"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,1,27]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>This paper investigates type-free axiomatic theories of positive truth. We derive the TKF system by strengthening specific axioms of the positive disquotational system PUTB and develop LKF by weakening certain axioms of the Kripke\u2013Feferman system KF. We establish that LKF\u2014which resolves some limitations of both PUTB and KF\u2014is equivalent to TKF. Furthermore, we provide specific standard models for LKF and examine its arithmetical and truth-theoretical strength. We further analyze variants of positive truth theories constructed by incorporating either the consistency axiom (CONS) or the completeness axiom (COMP), identifying a spectrum of positive truth systems spanning from PUTB to KF+CONS. Noteworthily, PUTB+CONS and PUTB+COMP suffice to prove the liar sentence and its negation, respectively. Our findings reveal that, with the exception of the weakest theory in this spectrum, the internal logics of positive truth theories cannot achieve both consistency and completeness. Finally, we argue that LKF+CONS serves as a more suitable system for deflationism than either PUTB or KF.<\/jats:p>","DOI":"10.1093\/jigpal\/jzag005","type":"journal-article","created":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T12:55:54Z","timestamp":1769086554000},"source":"Crossref","is-referenced-by-count":0,"title":["Notes on type-free axiomatic theories of positive truth"],"prefix":"10.1093","volume":"34","author":[{"given":"Dawei","family":"Liu","sequence":"first","affiliation":[{"name":"School of Philosophy , Hunan Normal University, Changsha, Hunan, 410081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Xiong","sequence":"additional","affiliation":[{"name":"Institute of Logic and Cognition , Department of Philosophy, Sun Yat-sen University, Guangzhou, Guangdong, 510275, 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