Dr. Purbita Jana from University of Calcutta will give a seminar on Thursday 22th of September 2016 starting form 11:00, in the Sala Riunioni of the Department of Mathematics.
Title: Fuzzy Topology via Fuzzy Geometric Logic with Graded Consequence.
Abstract: In this talk the main focus will be a generalization of Vickers’s work presented in his book \Topology via Logic”. Vickers introduced a notion of topological system which consists of a set of objects, set of properties and a relation between the set of objects and the set of properties satisfying certain conditions. Mathematically speaking a topological system is a triple consisting of a non-empty set, a frame and a relation, called a satisfaction relation. In this respect Vickers also relates the concept of topological system with so called geometric logic or logic of nite observations. In this talk fuzzy geometric logic and fuzzy geometric logic with graded consequence shall be discussed. Graded fuzzy topological system and fuzzy topological space with graded inclusion are obtained via fuzzy geometric logic with graded consequence. This work is a two-fold many-valued generalization of Vickers scheme viz., Topology via Logic, that naturally emerges from observational semantics. A categorical relationships among fuzzy topological space with graded inclusion, graded fuzzy topological system and graded frame shall be discussed. Categorical dualities among n-valued fuzzy Boolean system, n-valued fuzzy Boolean space and Lukasiewic n valued algebra with constants shall also be discussed.
