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SUMMARY:Quantitative equational reasoning - Prakash Panangaden\, McGill Un
 iversity
DTSTART:20180524T124500Z
DTEND:20180524T134500Z
UID:TALK106210@talks.cam.ac.uk
CONTACT:Victor Gomes
DESCRIPTION:Reasoning with equations is a central part of mathematics.  Ty
 pically we\nthink of solving equations but another role they play is to de
 fine\nalgebraic structures like groups or vector spaces.  Equational logic
  was\nformalized and developed by Birkhoff in the 1930s and led to a subje
 ct\ncalled universal algebra.  Universal algebra was used in formalizing\n
 concepts of data types in computer science.  In this talk I will present a
 \nquantitative analogue of equational logic: we write expressions like s =
 _ε\nt with the intended interpretation "s is within ε of t".  It turns o
 ut that\nthe metatheory of equational logic can be redeveloped in this set
 ting.\nPerhaps this seems like sterile theory but what makes it come alive
  is some\nstriking examples.  A notion of distance between probability dis
 tributions\ncalled the Kantorovich metric (frequently called the Wasserste
 in metric)\nhas become important in the theory of probabilistic systems an
 d in parts of\nmachine learning.  It turns out that this metric emerges na
 turally as the\n"free algebra" of some simple equational axioms in our ext
 ended sense.\nThis is joint work with Radu Mardare and Gordon Plotkin.
LOCATION:FW26
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