On categories with truth morphisms

• Grant number: 18/10326-4
• Support Opportunities: Scholarships abroad - Research
• Start date: March 01, 2019
• End date: June 30, 2019
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Edelcio Gonçalves de Souza
• Grantee: Edelcio Gonçalves de Souza
• Host Investigator: Otávio Augusto Santos Bueno
• Host Institution: Faculdade de Filosofia, Letras e Ciências Humanas (FFLCH). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: University of Miami, United States

Abstract

The aim of the present research project is to show how is possible to do semantic for propositional languages in a categorical setting dierent from topos. I propose the denition of two kinds of categories called categories with truth morphisms (CTM) and proto-topos. In categories with truth morphisms, it can be dened the truth functions that correspond to the logical connectives of negation, conjunction, implication and disjunction. In proto-topos, I show that the truth functions dened in CTM satisfy certain desirable properties with respect to the truth values true and false. I intend to study logical and meta mathematical properties satised by categories with truth morphisms and proto-topos. (AU)