Jefferson de Barros Santos Systems for Provability and Countermodel Generation in Propositional Minimal Implicational Logic Tese de Doutorado Thesis presented to the Programa de P´os-Gradua¸ c˜ ao em Inform´ atica of PUC-Rio in partial fulfillment of the requirements for the degree of Doutor em Ciˆ encias – Inform´ atica. Advisor : Prof. Edward Hermann Haeusler Co–Advisor: Prof. Gilles Dowek Rio de Janeiro May 2017