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| Author(s): |
Angela Pereira Rodrigues Moreira
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Filosofia e Ciências Humanas |
| Defense date: | 2016-07-04 |
| Examining board members: |
Itala Maria Loffredo D'Ottaviano;
Hercules de Araujo Feitosa;
Leandro Oliva Suguitani;
Marcelo Esteban Coniglio;
Edelcio Gonçalves de Souza
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| Advisor: | Itala Maria Loffredo D'Ottaviano |
| Abstract | |
Since the early decades of the twentieth century, translations between logics have been studied. The term "translation" was not always used, however. We highlighted as research pioneers in this area, Kolmogorov (1925), Glivenko (1929), Gödel (1933) and Gentzen (1933) as well as Prawitz and Malmnäs (1968), Brown and Suszko (1973), Szczerba (1977), Wójcicki (1988) and Epstein (1990); authors who have attempted to identify the main features of what we currently call translation between logics. In 1999, da Silva, D'Ottaviano and Sette proposed a very general definition for the concept of translation between logics. This definition tries to capture the intuition inherent to the "notion" of translation. Supervised by D'Ottaviano, Feitosa (1997), in his doctoral thesis, analyzed the concept of conservative translation and the category TrCon whose objects are the Tarski's logics and whose morphisms are the abstract conservative translations. Several articles have been published using these two concepts. In the "II World Congress on Universal Logic" (UNILOG'07), Carnielli, Coniglio and D'Ottaviano (2007) introduced the concept of contextual translation, simplifying the concept of meta-translation introduced by Coniglio (2005a). Recently, Je?ábek (2012) obtained results on the existence of conservative translation between any two deductive systems, which he identified as "reasonable", and pondered that it would take more refined criteria to define translations. In this thesis, in addition to having studied the historical articles about translations between logics, we analyzed recent studies in the literature on the subject. We introduced, based on the concept of contextual translation, the concept of abstract contextual translation and we obtained a necessary and sufficient condition for this new concept; we study a new category whose objects are the Tarski's logics and whose morphisms are the abstract contextual translations; we analyze the specificities and interrelations between the concepts of translation (da Silva, D'Ottaviano, Sette, 1999), conservative translation, contextual translation and abstract contextual translation and we relate these concepts to the concepts of (strict) contextual-conservative translation, hyper-contextual translation and isomorphism. We introduce the concepts of (strict) contextual-conservative translation and hyper-contextual translation from, respectively, the concepts of contextual translation and hypertranslation, the latter introduced by Figallo (2013). Finally, by analyzing the possible impact of Jerábek's article over the concept of conservative translation, we highlight the richness of the concept of conservative translation and the abundance of the category TrCon (AU) | |
| FAPESP's process: | 12/19683-8 - About translations between logics: Relations between conservative translations and contextual translations |
| Grantee: | Angela Pereira Rodrigues Moreira |
| Support Opportunities: | Scholarships in Brazil - Doctorate |