{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T17:37:57Z","timestamp":1782927477891,"version":"3.54.5"},"reference-count":45,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2022,2,10]],"date-time":"2022-02-10T00:00:00Z","timestamp":1644451200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,1,25]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Classical logic of formal provability includes L\u00f6b\u2019s theorem, but not reflection. In contrast, intuitions about the inferential behavior of informal provability (in informal mathematics) seem to invalidate L\u00f6b\u2019s theorem and validate reflection (after all, the intuition is, whatever mathematicians prove holds!). We employ a non-deterministic many-valued semantics and develop a modal logic T-BAT of an informal provability operator, which indeed does validate reflection and invalidates L\u00f6b\u2019s theorem. We study its properties and its relation to known provability-related paradoxical arguments. We also argue that T-BAT is a fairly sensible candidate for a formal logic of informal provability.<\/jats:p>","DOI":"10.1093\/jigpal\/jzab035","type":"journal-article","created":{"date-parts":[[2021,12,20]],"date-time":"2021-12-20T20:21:03Z","timestamp":1640031663000},"page":"172-193","source":"Crossref","is-referenced-by-count":5,"title":["Logic of informal provability with truth values"],"prefix":"10.1093","volume":"31","author":[{"given":"Pawel","family":"Pawlowski","sequence":"first","affiliation":[{"name":"Institute of Philosophy, University of Gdansk and CLPS , Ghent University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rafal","family":"Urbaniak","sequence":"additional","affiliation":[{"name":"Institute of Philosophy , University of 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