[logic-ml] ERATO Project Colloquium by Prakash Panangaden (10:00-11:30 on November 9th)

[Jeremy Dubut]

**

*Dear all,*

*

On Tuesday November 9th, Prakash Panangaden (McGill University, Canada) 
will give a talk, Quantitative Equational Logic, for our project 
colloquium from 10am (please note the unusual time). Further details can 
be found below.


If you would like to attend, please register through the following 
Google form:

https://forms.gle/6PoGNEfJVHLYDAdKA <https://forms.gle/6PoGNEfJVHLYDAdKA>

We later send you a zoom link by an email (using BCC).


For the latest information about ERATO colloquium / seminar, please see 
the webpage 
https://docs.google.com/document/d/1Qrg4c8XDkbO3tmns6tQwxn5lGHOrBON5LtHXXTpXDeA/edit?usp=sharing 
.


Jérémy Dubut (ERATO MMSD Colloquium Organizer)

Email: dubut at nii.ac.jp

-------*Tuesday November 9th, 10:00-11:30*


Speaker: *Prakash Panangaden (McGill University, Canada) *

Title: Quantitative Equational Logic


Abstract: Equations are at the heart of mathematical reasoning and 
reasoning with equations is the subject of equational logic. There are 
some landmark results in equational logic due to Birkhoff: the 
completeness theorem and the variety theorem. In the closely related 
subject of universal algebra there are results about algebraic 
structures defined equationally. Among these a major result is the 
existence of free algebras satisfying a universal property. In 
categorical terms, one can define monads on SET whose Eilenberg-Moore 
category gives the algebras and whose Kleisli category defines the free 
algebras. Together with Gordon Plotkin and Radu Mardare, we developed a 
theory of approximate equational reasoning by introducing the symbol =ε 
where ε is a (small) real number. One should think of s =ε t as meaning 
that s and t are within ε in some suitable sense. It turns out that one 
can define the notion of approximate equational reasoning and prove an 
analogue of the completeness theorem and the variety theorem. One can 
also define a quantitative algebra, which is an algebra equipped with a 
metric and give a construction of free algebras. This time the 
categorical description amounts to defining monads on EMET, the category 
of extended metric spaces and nonexpansive maps. More important than the 
theory is the existence of interesting examples that are very pertinent 
for probabilistic reasoning. There have been several interesting 
developments since the original paper in 2016. I will mention some of 
these but will not go into depth. Our work was aided by the 
contributions of Giorgio Bacci who played a major role in some of the 
later developments.

*
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