{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T21:48:59Z","timestamp":1772574539461,"version":"3.50.1"},"reference-count":47,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2021,4,21]],"date-time":"2021-04-21T00:00:00Z","timestamp":1618963200000},"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>We study the lattice of extensions of four-valued Belnap\u2013Dunn logic, called super-Belnap logics by analogy with superintuitionistic logics. We describe the global structure of this lattice by splitting it into several subintervals, and prove some new completeness theorems for super-Belnap logics. The crucial technical tool for this purpose will be the so-called antiaxiomatic (or explosive) part operator. The antiaxiomatic (or explosive) extensions of Belnap\u2013Dunn logic turn out to be of particular interest owing to their connection to graph theory: the lattice of finitary antiaxiomatic extensions of Belnap\u2013Dunn logic is isomorphic to the lattice of upsets in the homomorphism order on finite graphs (with loops allowed). In particular, there is a continuum of finitary super-Belnap logics. Moreover, a non-finitary super-Belnap logic can be constructed with the help of this isomorphism. As algebraic corollaries we obtain the existence of a continuum of antivarieties of De Morgan algebras and the existence of a prevariety of De Morgan algebras which is not a quasivariety.<\/jats:p>","DOI":"10.1017\/s1755020321000204","type":"journal-article","created":{"date-parts":[[2021,4,21]],"date-time":"2021-04-21T14:15:57Z","timestamp":1619014557000},"page":"114-163","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":8,"title":["THE LATTICE OF SUPER-BELNAP LOGICS"],"prefix":"10.1017","volume":"16","author":[{"given":"ADAM","family":"P\u0158ENOSIL","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,4,21]]},"reference":[{"key":"S1755020321000204_r16","unstructured":"[16] Dunn, J. M. (1969). Natural Language Versus Formal Language. 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