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SUMMARY:A formal context for metric semantics - Radu Mardare\, University 
 of Strathclyde
DTSTART:20211105T140000Z
DTEND:20211105T150000Z
UID:TALK163927@talks.cam.ac.uk
CONTACT:Jamie Vicary
DESCRIPTION:In the last decades the research in most of the fields in comp
 uter science\, from programming paradigms to cyber-physical systems and fr
 om robotics to learning\, has been challenged to integrate various concept
 s of continuous mathematics into semantics. This is because the interactio
 n of computational systems with the real world brought real-valued paramet
 ers in computation (rates\, probabilities\, differential equations\, time\
 , resources\, etc). And in this context\, the classic semantics centred on
  concepts of congruence (bisimulation\, behavioural equivalence) became in
 adequate. We are not interested anymore in understanding systems or their 
 behaviours up to identity\, but we need instead to work with approximation
 s of systems and of their behaviours\, which scale properly in the structu
 re of a computational system and allow us to understand approximated compu
 tation.\n\nTo answer this challenge\, we have introduced quantitative equa
 tional reasoning\, an algebraic theory that generalizes universal algebras
  by extending the classic concept of equation of type s=t to equations of 
 type s=_e t for some positive e\, interpreted as an upper bound of the dis
 tance between the interpretations of the terms s and t. In this way\, inst
 ead of axiomatizing congruences\, we axiomatize algebraic structures on me
 tric spaces. This provides the concepts we need to develop a metric semant
 ics for systems where the similarity between non-equivalent systems can be
  properly measured and approximated.\n\nThis talk is a tutorial on quantit
 ative equational reasoning and quantitative algebras. I plan to summarize 
 a series of results that we have published in the last five years\, joint 
 work with Prakash Panangaden and Gordon Plotkin.
LOCATION:FW26
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