AIAI Seminar - 15 May 2023 - Talk by Prakash Panangaden

Speaker:        Prakash Panangaden

Title:               Quantitative Equational Reasoning

Abstract: 

We develop a quantitative analogue of equational reasoning which we call quantitative algebra.  We define an equality relation indexed by rationals which we think of as capturing approximate equality.  This allows one to capture metric reasoning in a framework similar to equational reasoning.  The theory of equational logic and universal algebra extends smoothly to this metric setting.  We have several interesting examples where we have a quantitative equational theory whose free algebras correspond to well known structures.  In each case we have finitary and continuous versions.  Since its introduction in 2016 the theory has evolved rapidly and many new examples have been discovered.  I will present this topic from scratch so it should be widely accessible.

This is joint work with Giorgio Bacci, Radu Mardare and Gordon Plotkin.