{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T21:16:03Z","timestamp":1774127763665,"version":"3.50.1"},"reference-count":17,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":4334,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1995,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The aim of this paper is technically to study Belnap's four\u2010valued sentential logic (see [2]). First, we obtain a Gentzen\u2010style axiomatization of this logic that contains no structural rules while all they are still admissible in the Gentzen system what is proved with using some algebraic tools. Further, the mentioned logic is proved to be the least closure operator on the set of {\u039b, V, \u231d}\u2010formulas satisfying Tarski's conditions for classical conjunction and disjunction together with De Morgan's laws for negation. It is also proved that Belnap's logic is the only sentential logic satisfying the above\u2010mentioned conditions together with Anderson\u2010Belnap's Variable\u2010Sharing Property. Finally, we obtain a finite Hilbert\u2010style axiomatization of this logic. As a consequence, we obtain a finite Hilbert\u2010style axiomatization of Priest's logic of paradox (see [12]).<\/jats:p>","DOI":"10.1002\/malq.19950410403","type":"journal-article","created":{"date-parts":[[2007,6,2]],"date-time":"2007-06-02T20:51:52Z","timestamp":1180817512000},"page":"442-454","source":"Crossref","is-referenced-by-count":51,"title":["Characterizing Belnap's Logic via De Morgan's Laws"],"prefix":"10.1002","volume":"41","author":[{"given":"Alexej P.","family":"Pynko","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Distributive Lattices","author":"Balbes R.","year":"1974"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-1161-7_2"},{"key":"e_1_2_1_4_2","first-page":"60","article-title":"On finitely based consequence determined by a distributive lattice","volume":"9","author":"Dyrda K.","year":"1980","journal-title":"Bulletin Section of Logic, Polish Academy of Sciences"},{"key":"e_1_2_1_5_2","first-page":"124","article-title":"Characterization of the reduced matrices for the {\u039b V, V}\u2010fragment of classical logic","volume":"20","author":"Font J. 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