{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T09:39:27Z","timestamp":1776850767575,"version":"3.51.2"},"reference-count":60,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,10,30]],"date-time":"2024-10-30T00:00:00Z","timestamp":1730246400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,10,30]],"date-time":"2024-10-30T00:00:00Z","timestamp":1730246400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100005774","name":"Universitat de Barcelona","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100005774","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stud Logica"],"published-print":{"date-parts":[[2026,4]]},"abstract":"Abstract<\/jats:title>\n \n We determine the strictly positive fragment\n \n \n $$\\textsf{QPL}^+(\\textsf{HA})$$<\/jats:tex-math>\n \n \n \n QPL<\/mml:mi>\n +<\/mml:mo>\n <\/mml:msup>\n \n (<\/mml:mo>\n HA<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n of the quantified provability logic\n \n \n $$\\textsf{QPL}(\\textsf{HA})$$<\/jats:tex-math>\n \n \n QPL<\/mml:mi>\n (<\/mml:mo>\n HA<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n of Heyting Arithmetic. We show that\n \n \n $$\\textsf{QPL}^+(\\textsf{HA})$$<\/jats:tex-math>\n \n \n \n QPL<\/mml:mi>\n +<\/mml:mo>\n <\/mml:msup>\n \n (<\/mml:mo>\n HA<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is decidable and that it coincides with\n \n \n $$\\textsf{QPL}^+(\\textsf{PA})$$<\/jats:tex-math>\n \n \n \n QPL<\/mml:mi>\n +<\/mml:mo>\n <\/mml:msup>\n \n (<\/mml:mo>\n PA<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , which is the strictly positive fragment of the quantified provability logic of of Peano Arithmetic. This positively resolves a previous conjecture of the authors described in [14]. On our way to proving these results, we carve out the strictly positive fragment\n \n \n $$\\textsf{PL}^+(\\textsf{HA})$$<\/jats:tex-math>\n \n \n \n PL<\/mml:mi>\n +<\/mml:mo>\n <\/mml:msup>\n \n (<\/mml:mo>\n HA<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n of the provability logic\n \n \n $$\\textsf{PL}(\\textsf{HA})$$<\/jats:tex-math>\n \n \n PL<\/mml:mi>\n (<\/mml:mo>\n HA<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n of Heyting Arithmetic, provide a simple axiomatization, and prove it to be sound and complete for two types of arithmetical interpretations. The simple fragments presented in this paper should be contrasted with a recent result by Mojtahedi [43], where an axiomatization for\n \n \n $$\\textsf{PL}(\\textsf{HA})$$<\/jats:tex-math>\n \n \n PL<\/mml:mi>\n (<\/mml:mo>\n HA<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is provided. This axiomatization, although decidable, is of considerable complexity.\n <\/jats:p>","DOI":"10.1007\/s11225-024-10152-y","type":"journal-article","created":{"date-parts":[[2024,10,30]],"date-time":"2024-10-30T12:17:46Z","timestamp":1730290666000},"page":"263-295","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Strictly Positive Fragments of the Provability Logic of Heyting Arithmetic"],"prefix":"10.1007","volume":"114","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5152-198X","authenticated-orcid":false,"given":"Ana","family":"de Almeida Borges","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joost J.","family":"Joosten","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,10,30]]},"reference":[{"issue":"3","key":"10152_CR1","doi-asserted-by":"publisher","first-page":"1090","DOI":"10.2307\/2274475","volume":"55","author":"SN Artemov","year":"1990","unstructured":"Artemov, S.N., and G. 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