About translations between logics: Relations between conservative translations and contextual translations

• Grant number: 12/19683-8
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: January 01, 2013
• End date: December 31, 2015
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Itala Maria Loffredo D'Ottaviano
• Grantee: Angela Pereira Rodrigues Moreira
• Host Institution: Instituto de Filosofia e Ciências Humanas (IFCH). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 10/51038-0 - Logical consequence, reasoning and computation - LOGCONS, AP.TEM

Abstract

Since the early decades of the twentieth century interpretations between logics has been studied, and the term "translation" was not always used. We highlight as pioneers of researches in this area Kolmogorov (1925), Glivenko (1929), Lewis and Langford (1932), Gödel (1933) and Gentzen (1933). In 1999, da Silva, D'Ottaviano and Sette proposed a very general definition for the concept of translation between logics. Mentored by D'Ottaviano, Feitosa (1997), in his doctoral thesis, analyzed the concept of conservative translation and obtained important properties and applications of this class of translations. Have been published many articles 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. Recently JeYábek (2012) has obtained results on the existence of conservative translation between any two reasonable deductive systems and concluded that it would require criteria more refined to define translations. In this research project, in addition to studying historical articles about translations between logics, we analyze recent works of the literature on the subject. The objectives of this project are: obtain a necessary and sufficient condition that characterizes the contextual translations; analyze the specificities and possible interrelations between conservative translation and contextual translation; characterize a possible category whose objects are the Tarski's logics and whose morphisms are the contextual translations; and analyze possible impacts of the article of JeYábek (2012) in the concept of conservative translation.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

MOREIRA, Angela Pereira Rodrigues. About translations between logics: relations between conservative translations and abstract contextual translations. 2016. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Filosofia e Ciências Humanas Campinas, SP.