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CATEGORIES:Logic and Semantics Seminar (Computer Laboratory)
SUMMARY:Quantitative equational reasoning - Prakash Panang
aden\, McGill University
DTSTART;TZID=Europe/London:20180524T134500
DTEND;TZID=Europe/London:20180524T144500
UID:TALK106210AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/106210
DESCRIPTION:Reasoning with equations is a central part of math
ematics. Typically we\nthink of solving equations
but another role they play is to define\nalgebrai
c structures like groups or vector spaces. Equati
onal logic was\nformalized and developed by Birkho
ff in the 1930s and led to a subject\ncalled unive
rsal algebra. Universal algebra was used in forma
lizing\nconcepts of data types in computer science
. In this talk I will present a\nquantitative ana
logue of equational logic: we write expressions li
ke s =_ε\nt with the intended interpretation "s is
within ε of t". It turns out that\nthe metatheor
y of equational logic can be redeveloped in this s
etting.\nPerhaps this seems like sterile theory bu
t what makes it come alive is some\nstriking examp
les. A notion of distance between probability dis
tributions\ncalled the Kantorovich metric (frequen
tly called the Wasserstein metric)\nhas become imp
ortant in the theory of probabilistic systems and
in parts of\nmachine learning. It turns out that
this metric emerges naturally as the\n"free algebr
a" of some simple equational axioms in our extende
d sense.\nThis is joint work with Radu Mardare and
Gordon Plotkin.
LOCATION:FW26
CONTACT:Victor Gomes
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