Fuzzy topology via fuzzy geometric logic with graded consequence

In this paper fuzzy geometric logic and fuzzy geometric logic with graded consequence have been introduced. Graded fuzzy topological system and fuzzy topological space with graded inclusion are obtained via fuzzy geometric logic with graded consequence. As an offshoot, the notion of graded frame has been developed. This work is a two-fold many-valued generalization of Vickers' scheme 'Topology via Logic' and naturally emerges from observational semantics.