CATEGORIZING AND FUNCTORIALIZING LOGICAL TRANSLATIONS

• Grant number: 24/00087-3
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: July 01, 2024
• End date: May 31, 2029
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Itala Maria Loffredo D'Ottaviano
• Grantee: Angie Paola Hugueth Vásquez
• Host Institution: Instituto de Filosofia e Ciências Humanas (IFCH). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Logics may be understood as systems, algebras, spaces, or categories, depending on a chosen perspective (logical, algebraic, topological, categorical). We can also profit from many combinations of the various approaches, using correlative tools from category and topology, in particular, sheaves, topos, allegories, and intermediate categories. In these combinations, a functorial paradigm emerges, where adjoints, equivalences, isomorphisms, monads, allow to elucidate the structure of the logics involved. On another hand, translations between logics emphasize deductions and closure operators, capturing the logical-algebraic-topological characteristics of the logics involved. Orienting ourselves towards categorical contexts, translations become functors between categories, and one can try to use many constructions around functors and categorical hierarchization, in order to situate translations in a wider panorama. Our Ph.D. project circulates around a thorough and unifying study of the various mathematical layers present in logical translations. {\it Categorizing and functorializing logical translations} offers a good possibility to attain such an unification and deepening of perspectives. As a consequence of a Many-One, local-global, particular-universal, mathematical understanding of logical translations, we will also explore the philosophical significance of our layered categorical procedure.