{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T11:59:03Z","timestamp":1759147143013},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2021,4,20]],"date-time":"2021-04-20T00:00:00Z","timestamp":1618876800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2023,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Inquisitive first-order logic,<jats:sans-serif>InqBQ<\/jats:sans-serif>, is a system which extends classical first-order logic with formulas expressing questions. From a mathematical point of view, formulas in this logic express properties of sets of relational structures. This paper makes two contributions to the study of this logic. First, we describe an Ehrenfeucht\u2013Fra\u00efss\u00e9 game for<jats:sans-serif>InqBQ<\/jats:sans-serif>and show that it characterizes the distinguishing power of the logic. Second, we use the game to study cardinality quantifiers in the inquisitive setting. That is, we study what statements and questions can be expressed in<jats:sans-serif>InqBQ<\/jats:sans-serif>about the number of individuals satisfying a given predicate. As special cases, we show that several variants of the question<jats:italic>how many individuals satisfy<\/jats:italic><jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020321000198_inline1.png\"\/><jats:tex-math>$\\alpha (x)$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>are not expressible in<jats:sans-serif>InqBQ<\/jats:sans-serif>, both in the general case and in restriction to finite models.<\/jats:p>","DOI":"10.1017\/s1755020321000198","type":"journal-article","created":{"date-parts":[[2021,4,20]],"date-time":"2021-04-20T10:09:07Z","timestamp":1618913347000},"page":"241-267","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":3,"title":["GAMES AND CARDINALITIES IN INQUISITIVE FIRST-ORDER LOGIC"],"prefix":"10.1017","volume":"16","author":[{"given":"GIANLUCA","family":"GRILLETTI","sequence":"first","affiliation":[]},{"given":"IVANO","family":"CIARDELLI","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,4,20]]},"reference":[{"key":"S1755020321000198_r9","first-page":"35","article-title":"Sur quelques classifications des syst\u00e8mes de relations","volume":"1","author":"Fra\u00efss\u00e9","year":"1954","journal-title":"Publications Scientifiques de l\u2019Universit\u00e9 D\u2019Alger"},{"key":"S1755020321000198_r7","doi-asserted-by":"crossref","first-page":"281","DOI":"10.2307\/2271711","article-title":"An application of games to the completeness problem for formalized theories","volume":"32","author":"Ehrenfeucht","year":"1967","journal-title":"The Journal of Symbolic Logic"},{"key":"S1755020321000198_r6","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-linguistics-011817-045626"},{"key":"S1755020321000198_r17","first-page":"12","article-title":"On a generalization of quantifiers","volume":"44","author":"Mostowski","year":"1957","journal-title":"Foudations of Mathematics"},{"key":"S1755020321000198_r20","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-015-9379-1"},{"key":"S1755020321000198_r10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-52921-8_14"},{"key":"S1755020321000198_r14","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(82)90011-3"},{"key":"S1755020321000198_r5","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-010-9142-6"},{"key":"S1755020321000198_r23","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511974885"},{"key":"S1755020321000198_r2","unstructured":"[2] Ciardelli, I. (2016). Questions in Logic. Ph.D. Thesis, Institute for Logic, Language and Computation, University of Amsterdam."},{"key":"S1755020321000198_r8","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19750210112"},{"key":"S1755020321000198_r1","unstructured":"[1] Ciardelli, I. (2009). Inquisitive Semantics and Intermediate Logics. M.Sc. Thesis, University of Amsterdam."},{"volume-title":"A Shorter Model Theory","year":"1997","author":"Hodges","key":"S1755020321000198_r13"},{"key":"S1755020321000198_r25","doi-asserted-by":"publisher","DOI":"10.1007\/PL00003842"},{"volume-title":"fs","year":"2019","author":"Ciardelli","key":"S1755020321000198_r4"},{"key":"S1755020321000198_r16","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1111\/j.1755-2567.1966.tb00600.x","article-title":"First order predicate logic with generalized quantifiers","volume":"32","author":"Lindstr\u00f6m","year":"1966","journal-title":"Theoria"},{"key":"S1755020321000198_r19","doi-asserted-by":"publisher","DOI":"10.1007\/s10849-015-9219-2"},{"key":"S1755020321000198_r18","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/jzn011"},{"key":"S1755020321000198_r3","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-016-1221-y"},{"key":"S1755020321000198_r11","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-018-9835-3"},{"volume-title":"Knowledge and Belief: An Introduction to the Logic of the Two Notions","year":"1962","author":"Hintikka","key":"S1755020321000198_r12"},{"key":"S1755020321000198_r15","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)00025-X"},{"key":"S1755020321000198_r22","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-013-0282-4"},{"key":"S1755020321000198_r24","unstructured":"[24] van Benthem, J. (1976). Modal Correspondence Theory. Dissertation, Universiteit van Amsterdam, Instituut voor Logica en Grondslagenonderzoek van Exacte Wetenschappen, pp. 1\u2013148."},{"key":"S1755020321000198_r21","first-page":"409","volume-title":"Questions and Generalized Quantifiers","author":"Rexach","year":"1997"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020321000198","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,28]],"date-time":"2024-08-28T20:43:36Z","timestamp":1724877816000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020321000198\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,20]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["S1755020321000198"],"URL":"https:\/\/doi.org\/10.1017\/s1755020321000198","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"type":"print","value":"1755-0203"},{"type":"electronic","value":"1755-0211"}],"subject":[],"published":{"date-parts":[[2021,4,20]]},"assertion":[{"value":"\u00a9 The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}