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CATEGORIES:Logic and Semantics Seminar (Computer Laboratory)
SUMMARY:A formal context for metric semantics - Radu Marda
re\, University of Strathclyde
DTSTART;TZID=Europe/London:20211105T140000
DTEND;TZID=Europe/London:20211105T150000
UID:TALK163927AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/163927
DESCRIPTION:In the last decades the research in most of the fi
elds in computer science\, from programming paradi
gms to cyber-physical systems and from robotics to
learning\, has been challenged to integrate vario
us concepts of continuous mathematics into semanti
cs. This is because the interaction of computation
al systems with the real world brought real-valued
parameters in computation (rates\, probabilities\
, differential equations\, time\, resources\, etc)
. And in this context\, the classic semantics cent
red on concepts of congruence (bisimulation\, beha
vioural equivalence) became inadequate. We are not
interested anymore in understanding systems or th
eir behaviours up to identity\, but we need instea
d to work with approximations of systems and of th
eir behaviours\, which scale properly in the struc
ture of a computational system and allow us to und
erstand approximated computation.\n\nTo answer thi
s challenge\, we have introduced quantitative equa
tional reasoning\, an algebraic theory that genera
lizes universal algebras by extending the classic
concept of equation of type s=t to equations of ty
pe s=_e t for some positive e\, interpreted as an
upper bound of the distance between the interpreta
tions of the terms s and t. In this way\, instead
of axiomatizing congruences\, we axiomatize algebr
aic structures on metric spaces. This provides the
concepts we need to develop a metric semantics fo
r systems where the similarity between non-equival
ent systems can be properly measured and approxima
ted.\n\nThis talk is a tutorial on quantitative eq
uational reasoning and quantitative algebras. I pl
an to summarize a series of results that we have p
ublished in the last five years\, joint work with
Prakash Panangaden and Gordon Plotkin.
LOCATION:FW26
CONTACT:Jamie Vicary
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