{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:26:44Z","timestamp":1761611204680},"reference-count":12,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":5430,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1992,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper are studied the properties of the proofs in <jats:bold>PRA<\/jats:bold> of provability logic sentences, i.e. of formulas which are Boolean combinations of formulas of the form P<jats:sub>IPRA<\/jats:sub>(<jats:styled-content>h<\/jats:styled-content>), where <jats:styled-content>h<\/jats:styled-content> is the G\u00f6del\u2010number of a sentence in <jats:bold>PRA.<\/jats:bold> The main result is a Normal Form Theorem on the proof\u2010trees of provability logic sequents, which states that it is possible to split the proof into an arithmetical part, which contains only atomic formulas and has an essentially intuitionistic character, and into a logical part, which is merely instrumental. Moreover, the induction rules which occur in the arithmetical part are implicit. Some applications of the Normal Form Theorem are shown in order to obtain some syntactical results on the <jats:bold>PRA<\/jats:bold>\u2010completeness of modal logic. In particular a completeness theorem for Boolean combinations of modalities is given.<\/jats:p>","DOI":"10.1002\/malq.19920380150","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T05:51:06Z","timestamp":1180417866000},"page":"535-550","source":"Crossref","is-referenced-by-count":4,"title":["PROVABILITY LOGIC IN THE GENTZEN FORMULATION OF ARITHMETIC"],"prefix":"10.1002","volume":"38","author":[{"given":"Paolo","family":"Gentilini","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Gentilini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"The Unprovability of Consistency","author":"Boolos G.","year":"1979"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01371633"},{"key":"e_1_2_1_4_2","article-title":"Syntactical results on the arithmetic completeness of modal logic.","author":"Gentilini P.","journal-title":"Studia Logica."},{"key":"e_1_2_1_5_2","volume-title":"Collected Papers","author":"Gentzen G.","year":"1969"},{"key":"e_1_2_1_6_2","volume-title":"Proof Theory and Logical Complexity","author":"Girard J. Y.","year":"1987"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01700692"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.2307\/2266895"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.2307\/2269028"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00293433"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8601-8"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02757006"},{"key":"e_1_2_1_13_2","volume-title":"Proof Theory","author":"Takeuti G.","year":"1987"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19920380150","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19920380150","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T20:36:32Z","timestamp":1695846992000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19920380150"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/malq.19920380150"],"URL":"https:\/\/doi.org\/10.1002\/malq.19920380150","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,1]]}}}