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On categories with truth morphisms

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