{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T05:34:29Z","timestamp":1770960869781,"version":"3.50.1"},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2019,2,22]],"date-time":"2019-02-22T00:00:00Z","timestamp":1550793600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We shall be concerned with the modal logic BK\u2014which is based on the Belnap\u2013Dunn four-valued matrix, and can be viewed as being obtained from the least normal modal logic K by adding \u2018strong negation\u2019. Though all four values \u2018truth\u2019, \u2018falsity\u2019, \u2018neither\u2019 and \u2018both\u2019 are employed in its Kripke semantics, only the first two are expressible as terms. We show that expanding the original language of BK to include constants for \u2018neither\u2019 or\/and \u2018both\u2019 leads to quite unexpected results. To be more precise, adding one of these constants has the effect of eliminating the respective value at the level of BK-extensions. In particular, if one adds both of these, then the corresponding lattice of extensions turns out to be isomorphic to that of ordinary normal modal logics.<\/jats:p>","DOI":"10.1017\/s1755020319000121","type":"journal-article","created":{"date-parts":[[2019,2,22]],"date-time":"2019-02-22T11:36:14Z","timestamp":1550835374000},"page":"416-435","source":"Crossref","is-referenced-by-count":10,"title":["BELNAP\u2013DUNN MODAL LOGICS: TRUTH CONSTANTS VS. 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