{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T16:26:18Z","timestamp":1774628778834,"version":"3.50.1"},"reference-count":22,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T00:00:00Z","timestamp":1631059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"Russian Foundation for Basic Research","award":["20-01-00670"],"award-info":[{"award-number":["20-01-00670"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Logic"],"published-print":{"date-parts":[[2021,10,31]]},"abstract":"<jats:p>\n            Let\n            <jats:italic>V<\/jats:italic>\n            be a set of number-theoretical functions. We define a notion of absolute\n            <jats:italic>V<\/jats:italic>\n            -realizability for predicate formulas and sequents in such a way that the indices of functions in\n            <jats:italic>V<\/jats:italic>\n            are used for interpreting the implication and the universal quantifier. In this article, we prove that Basic Predicate Calculus is sound with respect to the semantics of absolute\n            <jats:italic>V<\/jats:italic>\n            -realizability if\n            <jats:italic>V<\/jats:italic>\n            satisfies some natural conditions.\n          <\/jats:p>","DOI":"10.1145\/3468856","type":"journal-article","created":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T19:02:44Z","timestamp":1631127764000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Generalized Realizability and Basic Logic"],"prefix":"10.1145","volume":"22","author":[{"given":"Aleksandr Yu.","family":"Konovalov","sequence":"first","affiliation":[{"name":"Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russian Federation"}]}],"member":"320","published-online":{"date-parts":[[2021,9,8]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1005196310070"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.2307\/2275700"},{"key":"e_1_2_1_3_1","first-page":"4","article-title":"Minimal realizability of intuitionistic arithmetic and elementary analysis","volume":"60","author":"Damnjanovic Zlatan","year":"1995","unstructured":"Zlatan Damnjanovic . 1995 . Minimal realizability of intuitionistic arithmetic and elementary analysis . J. Symbol. Log. 60 , 4 (Dec. 1995), 1208\u20131241. https:\/\/doi.org\/10.2307\/2275884 10.2307\/2275884 Zlatan Damnjanovic. 1995. Minimal realizability of intuitionistic arithmetic and elementary analysis. J. Symbol. Log. 60, 4 (Dec. 1995), 1208\u20131241. https:\/\/doi.org\/10.2307\/2275884","journal-title":"J. Symbol. Log."},{"key":"e_1_2_1_4_1","first-page":"4","article-title":"On the interpretation of intuitionistic number theory","volume":"10","author":"Kleene Stephen C.","year":"1945","unstructured":"Stephen C. Kleene . 1945 . On the interpretation of intuitionistic number theory . J. Symbol. Log. 10 , 4 (Dec. 1945), 109\u2013124. https:\/\/doi.org\/10.2307\/2269016 10.2307\/2269016 Stephen C. Kleene. 1945. On the interpretation of intuitionistic number theory. J. Symbol. Log. 10, 4 (Dec. 1945), 109\u2013124. https:\/\/doi.org\/10.2307\/2269016","journal-title":"J. Symbol. Log."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.3103\/S0027132216010071"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.3103\/S0027132216040069"},{"key":"e_1_2_1_7_1","first-page":"41","article-title":"The intuitionistic logic is not sound with respect to L-realizability","volume":"22","author":"Konovalov Aleksandr Yu.","year":"2018","unstructured":"Aleksandr Yu. Konovalov . 2018 . The intuitionistic logic is not sound with respect to L-realizability . Intell. Syst. Theor. Applic. 22 , 3 (2018), 41 \u2013 44 . Retrieved from http:\/\/mi.mathnet.ru\/ista148 Aleksandr Yu. Konovalov. 2018. The intuitionistic logic is not sound with respect to L-realizability. Intell. Syst. Theor. Applic. 22, 3 (2018), 41\u201344. Retrieved from http:\/\/mi.mathnet.ru\/ista148","journal-title":"Intell. Syst. Theor. 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Doklady Akad Nauk SSSR 214, 3 (1974), 520\u2013523. http:\/\/mi.mathnet.ru\/eng\/dan38065.","journal-title":"Doklady Akad Nauk SSSR"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1070\/IM1977v011n03ABEH001731"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1070\/IM1984v022n02ABEH001444"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.5555\/28907"},{"key":"e_1_2_1_20_1","first-page":"121","article-title":"Basic logic and Fregean set theory","volume":"5","author":"Ruitenburg Wim","year":"1993","unstructured":"Wim Ruitenburg . 1993 . Basic logic and Fregean set theory . Dirk Van Dalen Festschrift, Quaestiones Infinitae 5 (1993), 121 \u2013 142 . Retrieved from https:\/\/www.mscsnet.mu.edu\/ wim\/publica\/120519_baslog.pdf Wim Ruitenburg. 1993. Basic logic and Fregean set theory. Dirk Van Dalen Festschrift, Quaestiones Infinitae 5 (1993), 121\u2013142. 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