Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2018-03-02T23:39:14Z No. of bitstreams: 1 ThiagoNascimentoDaSilva_DISSERT.pdf: 675458 bytes, checksum: 9123812e69a846020d3cd6346e530e1e (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2018-03-13T18:55:45Z (GMT) No. of bitstreams: 1 ThiagoNascimentoDaSilva_DISSERT.pdf: 675458 bytes, checksum: 9123812e69a846020d3cd6346e530e1e (MD5) / Made available in DSpace on 2018-03-13T18:55:45Z (GMT). No. of bitstreams: 1 ThiagoNascimentoDaSilva_DISSERT.pdf: 675458 bytes, checksum: 9123812e69a846020d3cd6346e530e1e (MD5) Previous issue date: 2018-01-25 / Al?m da mais conhecida l?gica de Nelson (?3) e da l?gica paraconsistente de Nelson (?4), David Nelson introduziu no artigo de 1959 "Negation and separation of concepts in constructive systems", com motiva??es de aritm?tica e construtividade, a l?gica que ele chamou de "?". Naquele trabalho, a l?gica ? definida por meio de um c?lculo (que carece crucialmente da regra de contra??o) tendo infinitos esquemas de regras, e nenhuma sem?ntica ? fornecida. Neste trabalho n?s tomamos o fragmento proposicional de ?, mostrando que ele ? algebriz?vel (de fato, implicativo) no sentido de Blok & Pigozzi com respeito a uma classe de reticulados residuados involutivos. Assim, fornecemos a primeira sem?ntica para ? (que chamamos de ?-?lgebras), bem como um c?lculo estilo Hilbert finito equivalente ? apresenta??o de Nelson. Fornecemos um algoritmo para construir ?-?lgebras a partir de ?-?lgebras ou reticulados implicativos e demonstramos alguns resultados sobre a classe de ?lgebras que introduzimos. N?s tamb?m comparamos ? com outras l?gicas da fam?lia de Nelson, a saber, ?3 e ?4. / Besides the better-known Nelson logic (?3) and paraconsistent Nelson logic (?4), in Negation and separation of concepts in constructive systems (1959) David Nelson introduced a logic that he called ?, with motivations of arithmetic and constructibility. The logic was defined by means of a calculus (crucially lacking the contraction rule) having infinitely many rule schemata, and no semantics was provided for it. We look in the present dissertation at the propositional fragment of ?, showing that it is algebraizable (in fact, implicative) in the sense of Blok and Pigozzi with respect to a class of involutive residuated lattices. We thus provide the first known algebraic semantics for ?(we call them of ?-algebras) as well as a finite Hilbert-style calculus equivalent to Nelson?s presentation. We provide an algorithm to make ?-algebras from ?-algebras or implicative lattices and we prove some results about the class of algebras which we have introduced. We also compare ? with other logics of the Nelson family, that is, ?3 and ?4.