{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T22:04:29Z","timestamp":1747173869853,"version":"3.40.5"},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T00:00:00Z","timestamp":1695859200000},"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":[[2024,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper puts forth a class of algebraic structures, <jats:italic>relativized Boolean algebras<\/jats:italic> (RBAs), that provide semantics for propositional logic in which truth\/validity is only defined relative to a local domain. In particular, the join of an event and its complement need not be the top element. Nonetheless, behavior is locally governed by the laws of propositional logic. By further endowing these structures with operators\u2014akin to the theory of modal Algebras\u2014RBAs serve as models of modal logics in which truth is relative. In particular, modal RBAs provide semantics for various well-known awareness logics and an alternative view of possibility semantics.<\/jats:p>","DOI":"10.1017\/s1755020323000308","type":"journal-article","created":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T09:14:21Z","timestamp":1695892461000},"page":"154-177","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["ALGEBRAIC SEMANTICS FOR RELATIVE TRUTH, AWARENESS, AND POSSIBILITY"],"prefix":"10.1017","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4189-5504","authenticated-orcid":false,"given":"EVAN","family":"PIERMONT","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2023,9,28]]},"reference":[{"doi-asserted-by":"publisher","key":"S1755020323000308_r3","DOI":"10.2307\/2998545"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r14","DOI":"10.1016\/j.jet.2008.10.001"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r13","DOI":"10.2307\/2269810"},{"volume-title":"Object-Based Unawareness","year":"2007","author":"Board","key":"S1755020323000308_r1"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r12","DOI":"10.4288\/jafpos1956.10.139"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r5","DOI":"10.1090\/S0002-9939-1951-0045084-7"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r17","DOI":"10.1006\/game.1998.0666"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r7","DOI":"10.1016\/j.geb.2007.01.012"},{"key":"S1755020323000308_r21","first-page":"1353","article-title":"A bimodal perspective on possibility semantics","volume":"27","author":"van Benthem","year":"2016","journal-title":"Journal of Logic and Computation"},{"volume-title":"The Stanford Encyclopedia of Philosophy","year":"2018","author":"Monk","key":"S1755020323000308_r18"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r8","DOI":"10.1016\/j.geb.2009.02.001"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r9","DOI":"10.1016\/j.mathsocsci.2012.08.003"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r20","DOI":"10.1305\/ndjfl\/1093893943"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r10","DOI":"10.1016\/j.jet.2005.02.007"},{"key":"S1755020323000308_r2","first-page":"183","article-title":"The concept of quasi-truth","volume":"39","author":"Bueno","year":"1996","journal-title":"Logique et Analyse"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r6","DOI":"10.1609\/aaai.v33i01.33012851"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r4","DOI":"10.1016\/0004-3702(87)90003-8"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r11","DOI":"10.1016\/j.geb.2007.07.003"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r15","DOI":"10.1007\/BF00293423"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r16","DOI":"10.1007\/BF01079207"},{"doi-asserted-by":"publisher","key":"S1755020323000308_r19","DOI":"10.1007\/BF00258428"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020323000308","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,26]],"date-time":"2024-03-26T09:48:35Z","timestamp":1711446515000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020323000308\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,28]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["S1755020323000308"],"URL":"https:\/\/doi.org\/10.1017\/s1755020323000308","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"type":"print","value":"1755-0203"},{"type":"electronic","value":"1755-0211"}],"subject":[],"published":{"date-parts":[[2023,9,28]]},"assertion":[{"value":"\u00a9 The Author(s), 2023. 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