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The logic $\\mathcal{S}$ was originally presented by means of a calculus (crucially lacking the contraction rule) with infinitely many rule schemata and no semantics (other than the intended interpretation into Arithmetic). We look here at the propositional fragment of $\\mathcal{S}$, showing that it is algebraizable (in fact, implicative), in the sense of Blok and Pigozzi, with respect to a variety of three-potent involutive residuated lattices. We thus introduce the first known algebraic semantics for $\\mathcal{S}$ as well as a finite Hilbert-style calculus equivalent to Nelson\u2019s presentation; this also allows us to clarify the relation between $\\mathcal{S}$ and the other two Nelson logics $\\mathcal{N}3$ and $\\mathcal{N}4$.<\/jats:p>","DOI":"10.1093\/jigpal\/jzaa015","type":"journal-article","created":{"date-parts":[[2020,3,6]],"date-time":"2020-03-06T12:25:28Z","timestamp":1583497528000},"page":"1182-1206","source":"Crossref","is-referenced-by-count":3,"title":["Nelson\u2019s logic \ud835\udcae"],"prefix":"10.1093","volume":"28","author":[{"given":"Thiago","family":"Nascimento","sequence":"first","affiliation":[{"name":"Programa de P\u00f3s-Gradua\u00e7\u00e3o em Sistemas e Computa\u00e7\u00e3o, Universidade Federal do Rio Grande do Norte, 59078-970 Natal, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Umberto","family":"Rivieccio","sequence":"additional","affiliation":[{"name":"Departamento 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