{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T05:35:51Z","timestamp":1757309751664},"reference-count":31,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T00:00:00Z","timestamp":1619136000000},"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":[[2023,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Here, I combine the semantics of Mares and Goldblatt [20] and Seki [29, 30] to develop a semantics for quantified modal relevant logics extending <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020321000216_inline1.png\" \/><jats:tex-math>\n${\\bf B}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. The combination requires demonstrating that the Mares\u2013Goldblatt approach is apt for quantified extensions of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020321000216_inline2.png\" \/><jats:tex-math>\n${\\bf B}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and other relevant logics, but no significant bridging principles are needed. The result is a single semantic approach for quantified modal relevant logics. Within this framework, I discuss the requirements a quantified modal relevant logic must satisfy to be \u201csufficiently classical\u201d in its modal fragment, where frame conditions are given that work for positive fragments of logics. The roles of the Barcan formula and its converse are also investigated.<\/jats:p>","DOI":"10.1017\/s1755020321000216","type":"journal-article","created":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T08:19:59Z","timestamp":1619165999000},"page":"210-240","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":7,"title":["QUANTIFIED MODAL RELEVANT LOGICS"],"prefix":"10.1017","volume":"16","author":[{"given":"NICHOLAS","family":"FERENZ","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,4,23]]},"reference":[{"key":"S1755020321000216_r23","doi-asserted-by":"publisher","DOI":"10.26686\/ajl.v8i0.1812"},{"key":"S1755020321000216_r13","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-009-9109-7"},{"key":"S1755020321000216_r7","first-page":"1","volume-title":"Handbook of Philosophical Logic","author":"Dunn","year":"2002"},{"key":"S1755020321000216_r8","doi-asserted-by":"publisher","DOI":"10.1007\/BF00249674"},{"key":"S1755020321000216_r12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-9084-4_2"},{"key":"S1755020321000216_r14","first-page":"227","article-title":"A general semantics for quantified modal logic","volume":"6","author":"Goldblatt","year":"2006","journal-title":"Advances in Modal Logic"},{"key":"S1755020321000216_r9","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-1005-8_16"},{"key":"S1755020321000216_r28","volume-title":"An Essay in Classical Modal Logic.","author":"Segerberg","year":"1971"},{"key":"S1755020321000216_r29","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1082637806"},{"key":"S1755020321000216_r31","doi-asserted-by":"publisher","DOI":"10.2307\/2272558"},{"key":"S1755020321000216_r18","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19930390119"},{"key":"S1755020321000216_r15","volume-title":"Algebraic Logic","author":"Halmos","year":"1962"},{"key":"S1755020321000216_r25","doi-asserted-by":"publisher","DOI":"10.1007\/BF00649991"},{"key":"S1755020321000216_r26","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71541-6"},{"key":"S1755020321000216_r24","doi-asserted-by":"publisher","DOI":"10.4324\/9780203016244"},{"key":"S1755020321000216_r22","doi-asserted-by":"publisher","DOI":"10.1007\/BF01049182"},{"key":"S1755020321000216_r16","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-018-9493-y"},{"key":"S1755020321000216_r1","volume-title":"Entailment: The Logic of Relevance and Necessity","author":"Anderson","year":"1975"},{"key":"S1755020321000216_r27","volume-title":"Relevant Logics and Their Rivals: Part 1. 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