{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T14:29:54Z","timestamp":1695911394338},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2021,3,8]],"date-time":"2021-03-08T00:00:00Z","timestamp":1615161600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We take <jats:italic>Carnap\u2019s problem<\/jats:italic> to be to what extent standard consequence relations in various formal languages fix the meaning of their logical vocabulary, alone or together with additional constraints on the form of the semantics. This paper studies Carnap\u2019s problem for basic modal logic. Setting the stage, we show that neighborhood semantics is the most general form of compositional possible worlds semantics, and proceed to ask which standard modal logics (if any) constrain the box operator to be interpreted as in relational Kripke semantics. Except when restricted to finite domains, no modal logic characterizes exactly the Kripkean interpretations of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020321000083_inline1.png\" \/><jats:tex-math>\n$\\Box $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Moreover, we show that, in contrast with the case of first-order logic, the obvious requirement of permutation invariance is not adequate in the modal case. After pointing out some known facts about modal logics that nevertheless force the Kripkean interpretation, we focus on another feature often taken to embody the gist of modal logic: locality. We show that invariance under point-generated subframes (properly defined) does single out the Kripkean interpretations, but only among topological interpretations, not in general. Finally, we define a notion of bisimulation invariance\u2014another aspect of locality\u2014that, together with a reasonable closure condition, gives the desired general result. Along the way, we propose a new perspective on normal neighborhood frames as filter frames, consisting of a set of worlds equipped with an accessibility relation, and a free filter at every world.<\/jats:p>","DOI":"10.1017\/s1755020321000083","type":"journal-article","created":{"date-parts":[[2021,3,8]],"date-time":"2021-03-08T05:17:47Z","timestamp":1615180667000},"page":"578-602","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["CARNAP\u2019S PROBLEM FOR MODAL LOGIC"],"prefix":"10.1017","volume":"16","author":[{"given":"DENIS","family":"BONNAY","sequence":"first","affiliation":[]},{"given":"DAG","family":"WESTERST\u00c5HL","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,3,8]]},"reference":[{"key":"S1755020321000083_r11","doi-asserted-by":"publisher","DOI":"10.2307\/2372123"},{"key":"S1755020321000083_r1","first-page":"41","volume-title":"The Semantic Conception of Logic","author":"Bonnay","year":"2021"},{"key":"S1755020321000083_r22","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5587-4_5"},{"key":"S1755020321000083_r20","doi-asserted-by":"publisher","DOI":"10.2307\/2272167"},{"key":"S1755020321000083_r3","volume-title":"Formalization of Logic","volume":"2","author":"Carnap","year":"1943"},{"key":"S1755020321000083_r25","first-page":"517","article-title":"The adequacy problem for classical logic","volume":"7","author":"Zucker","year":"1978","journal-title":"Journal of Philosophical Logic"},{"key":"S1755020321000083_r5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02770513"},{"key":"S1755020321000083_r7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-18362-6_2"},{"key":"S1755020321000083_r8","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700041186"},{"key":"S1755020321000083_r23","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020316000447"},{"key":"S1755020321000083_r24","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-9407-2_9"},{"key":"S1755020321000083_r9","first-page":"151","volume-title":"Modality, Morality, and Other Problems of Sense and Nonsense; Essays Dedicated to S\u00f6ren Halld\u00e9n","author":"Hansson","year":"1973"},{"key":"S1755020321000083_r10","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020317000259"},{"key":"S1755020321000083_r13","unstructured":"13 MacFarlane, J. (2000). What Does It Mean to Say That Logic Is Formal? Ph.D. Thesis, University of Pittsburgh."},{"key":"S1755020321000083_r2","doi-asserted-by":"publisher","DOI":"10.1007\/s10670-015-9764-8"},{"key":"S1755020321000083_r17","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-3272-8_7"},{"key":"S1755020321000083_r4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511621192"},{"key":"S1755020321000083_r6","first-page":"65","volume-title":"Id\u00e9es Fixes: A Festschrift Dedicated to Christian Bennet on the Occasion of his 60 th Birthday","author":"Engstr\u00f6m","year":"2014"},{"key":"S1755020321000083_r12","unstructured":"12 Litak, T. (2018). On a problem of Westerst\u00e5hl (manuscript)."},{"key":"S1755020321000083_r15","first-page":"102","volume-title":"Contemporary Philosophy: A Survey","author":"Montague","year":"1968"},{"key":"S1755020321000083_r16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-67149-9"},{"key":"S1755020321000083_r14","first-page":"252","article-title":"Some embedding theorems for modal logic","volume":"XII","author":"Makinson","year":"1971","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S1755020321000083_r19","doi-asserted-by":"publisher","DOI":"10.1111\/j.1755-2567.1980.tb00696.x"},{"key":"S1755020321000083_r21","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093635152"},{"key":"S1755020321000083_r18","volume-title":"An Essay in Classical Modal Logic","author":"Segerberg","year":"1971"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020321000083","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,16]],"date-time":"2023-05-16T10:34:21Z","timestamp":1684233261000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020321000083\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,8]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["S1755020321000083"],"URL":"https:\/\/doi.org\/10.1017\/s1755020321000083","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,8]]},"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"}}]}}