Applications of supported quantales to modal logic

Preface This document is the report of my final degree project. The project consisted of an initiation to research: an unsolved mathematical problem was presented to me by my project tutor Pedro Resende, and my task was to help find a solution for it. This eventually led to writing a scientific paper with him as a co-author. This paper is currently in preparation and once finished it will be submitted to a journal in mathematics. In the present report I describe the results which are or will be contained in the article, along with some motivation and technical background. I take this opportunity to thank all professors that crossed my academic path and in some way enriched my knowledge and way of thinking, especially to my tutor for all his guidance, patience and enthusiasm throughout this last year. I want also to thank to the CLC (Center for Logic and Computation, Instituto Superior Técnico), of which I have been a student member since March, for the support and extra motivation that their kindly invitation represented.