GUILHERME MESSIAS PEREIRA LIMA

It’s usual to analytical philosophers to use, implicitly or explicitly, logical formalization in their arguments, it aims to regulate valid inferences in certain rational contexts; for instance, modal logic is used to represent metaphysical notions. But the very adoption of a logical system demands philosophical assumptions. The relationship between topological spaces and the propositional modal system S4 is known since 1944. In 2008, Awodey and Kishida [08] demonstrated that the logic FOS4 is complete concerning for the class of sheaf-interpretations, bundle interpretations with topological structure. In this project, we investigate the topological properties of those semantics for S4 and FOS4. Such systems are locally similar to Euclidean spaces.