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Doctoral Thesis
Full name
Diogo Henrique Bispo Dias
Knowledge Area
Date of Defense
São Paulo, 2019
Souza, Edelcio Gonçalves de (President)
Bueno, Otavio Augusto Santos
Leite, Alexandre Fernandes Batista Costa
Silva, Rodrigo Bacellar da Costa e
Title in Portuguese
Paraconsistentização de lógicas
Keywords in Portuguese
Lógicas paraconsistentes
Pluralismo lógico
Abstract in Portuguese
Esta tese tem como objetivo estudar a paraconsistentização de lógicas, que consiste em encontrar, para uma dada lógica, sua contraparte paraconsistente. A estratégia geral utilizada para tal tarefa é: ao encontrar premissas inconsistentes, faça inferências a partir de seus subconjuntos consistentes. Para isso, foram desenvolvidos dois métodos de paraconsistentização. O primeiro consiste na utilização do arcabouço teórico da Teoria de Categorias, enquanto que o segundo faz uso da teoria da prova e da noção de estruturas valorativas. Após a apresentação dos métodos, algumas propriedades formais de ambas as propostas foram investigadas. Em particular, provou-se que a paraconsistentização preserva correção e completude, isto é, se a lógica inicial for correta e completa, sua contraparte paraconsistente também o será. Também foram estabelecidas as condições suficientes que uma lógica deve satisfazer para poder ser paraconsistentizada. A partir destes resultados, os dois métodos propostos foram comparados com outras abordagens desenvolvidas para raciocinar a partir de conjuntos inconsistentes. Por fim, a tese analisa o debate entre pluralismo e monismo lógico investigando, especificamente, as contribuições da paraconsistentização para tal discussão.
Title in English
Paraconsistentization of logics
Keywords in English
Logical monism
Logical pluralism
Paraconsistent logics
Abstract in English
This thesis aims to study the paraconsistentization of logics, which consists in finding, for a given logic, its paraconsistent counterpart. The general strategy used for this task is the following: when finding inconsistent premises, one must draw inferences from its consistent subsets. For this, two methods of paraconsistentization were developed. The first consists in using the framework of Category Theory, while the second one makes use of proof theory and the notion of valuation structure. After their presentation, some formal properties of both proposals were investigated. In particular, it was proved that paraconsistentization preserves soundness and completeness, that is, if the initial logic is sound and complete, its paraconsistent counterpart will also be. The sufficient conditions that a logic must satisfy in order for it to be paraconsistentized were also established. From these results, the two proposed methods were compared with other approaches developed to reason from inconsistent sets. Finally, the thesis analyses the debate between pluralism and logical monism investigating, specifically, the contributions of paraconsistentization to this discussion.
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