A categorical approach to continuous logic using MV-algebras

Abstract

Continuous logic was first defined in 2008 as a new logic designed to study metric spaces. Taking elements from several other logics, one of the core principles is the fact that the truth space is the interval [0,1]. Moreover, continuous logic can be seen as a generalization of classical first order logic. More recently there has been some research into applying category theory to continuous logic. Last year in particular, Daniël Figueroa (UvA) analysed continuous logic in his master thesis using the concept of hyperdoctrines, but as he pointed out his analysis had some flaws. In my thesis I discussed his analysis and presented my own approach, which involves MV-algebras.