Talk at the Logic Mentoring Workshop, LiCS 2017

1. +
Weapons of Math Construction:
Proofs for Programs and Personal
Assistants
Valeria de Paiva
Nuance Communications, Sunnyvale, CA

2. +
What a title!

3. +
Minas Gerais, Brazil
Personal and inspiring?

4. +
PUC—Rio de Janeiro
Maths Dept

5. +
University of Cambridge
Pure Maths (old DPMMS)

6. +
University of Cambridge
Pure Maths (old DPMMS)

7. +
University of Cambridge
Pure Maths (DPMMS)
Dialectica Categories PhD thesis
Gödel: consistency of Arithmetic.
Internal categorical model Dialectica!
(very precise) models of Linear Logic.

8. +University of Cambridge

9. +
University of Cambridge
Computer Laboratory
1989-1995
Formalizing and proving about automated reasoning:
subtyping and dependent types
Acquisition of Lexical Semantics, Machine Readable Dictionaries, Acquilex
Constructive Modal Logic and properties of programs
Authentication and authorization logics

10. +
University of Birmingham, UK
Computer Science - professor

11. +
Birmingham & xSLAM project
Explicit Substitutions
Linear functional Programming
Constructive Necessity
Intuitionistic and Linear Calculus
Full Intuitionistic Linear Logic
Constructive Hybrid Logic, etc

12. +
NLTT: Natural Language Theory
and Technology
October 2000-May 2008

13. +
NLTT: Natural Language Theory
and Technology
1999-2008
KXDC (Knowledge eXtraction from Document Collections)
NIMD (Novel Intelligence from Massive Data)
AQUAINT (Advanced Question Answering from Text)

14. +
PowerSet and Spin Outs

15. +
NLTT: Natural Language Theory
and Technology
n Spinning out technology is a
tradition
n Split out the group
n Take a plunge!

17. +
Adventures in Searchland
PARC Forum
n Valeria de Paiva, Cuil,
Search Analyst
n 30 July 2009
4:00-5:00pm
George E. Pake Auditorium,
PARC, Palo Alto, CA
map/ directions
n http://www.parc.com/event/9
34/adventures-in-
searchland.html
n Video and audio

18. +
Launching a hot
product…

19. +
After the hype, the blogsphere….

20. +The reasons for Cuil
l There is (too much) information on the web.
l Cuil 'organized' the web so that you can find information that you
didn't know you wanted..

21. +The reasons are still there…
l Reports estimate we can see only 15% of the existing web.
l Probing the web is mostly popularity based.You're likely to see
what others have seen before. But your seeing increases the
popularity of what you saw, thereby reducing the pool of
available stuff.
l Vicious or virtuous circle? How to measure?
l Eli Pariser,The Filter Bubble, book and TED talk,
www.ted.com/talks/eli_pariser_beware_online_filter_bubbles.html
But asYahoo shows, the barrier is every time higher…

22. +
The Financial Crisis

23. +
Rearden Commerce? ...

24. +
Rearden Commerce, Foster City,
CA, 2011-2012
n Whitelabelling travelling systems
n Ontologies/Reasoning for travelling
systems
n Sentiment analysis
n Coordinating reviews annotations
analytics
n Predicting customers’ wishes?

25. +
Nuance Comms,
AI and NL Lab, Sunnyvale, CA
2012-now

26. +
The Future is Meaning…

27. +
Unity Behind Disparity:
Proofs are Programs?...

29. +
Curry-Howard Correspondence
Triangles
Lambda-
calculus
Intuitionistic
Propositional
Logic
Cartesian
Closed
Categories
1963 1965

30. +How do I get into this picture?

31. +Same triangle...different logic
Linear Logic, a proof theoretic logic
described by Jean-Yves Girard in
1986.
Basic idea: assumptions cannot be
discarded or duplicated.They must
be used exactly once—just like dollar
bills...
Other approaches to accounting for
logical resources. Great win of Linear
Logic:
Account for resources when you want to,
otherwise fall back on traditional
logic,
A=>B iff !A –o B

32. +
Curry-Howard Correspondence
Linear
Lambda-
Calculus
Linear
Logic
Linear
Categories

33. +
Curry-Howard Correspondence
TriangleS
Functional
Programming
Proof Theory
Category
Theory
How many? Which applications? Reactive Functional programming?
Android apps race conditions? Rust and effect calculus?

34. +My example: Dialectica categories
Linear Lambda
Calculus
(Int) Linear
Logic
Dialectica
Categories

35. +(many )More Dialectica Categories
Models of Petri nets: (with Brown and Gurr)
Lambek calculus version (linguistics), Amsterdam Colloquium
State in imperative programming, (Correa et al, after Reddy)
Generic models of Linear Logic (with Schalk,TCS2004)
P. Oliva and collaborators, Dialectica for functional interpretations
Cardinalities of the Continuum and Combinatorics of Ideals,
Samuel G. da Silva, Set Theory, 2017
Dialectica Interpretations: A Categorical Analysis, B. Biering, 2008
The dialectica monad and its cousins, Pieter J.W. Hofstra, 2011
Budiu, Galenson, Plotkin.The Compiler Forest, ESOP 2013
Functional Functional Interpretation, Pierre-Marie Pedrot, LICS14

36. +
Bridges?
Translation

37. +
The Future is Meaning
http://www.wired.com/2013/03/conversational-user-interface/

38. Siri
Oct 2011
Google Now
Jul 2012
Nina
Aug 2012
USAA EVA
CVS
Cortana
Aug 2014
Dom
Oct 2014
USAA Coach
May 2015
Voice based Virtual Assistants paving
the way for general acceptance of AI
INGE
Lily
May 2013
Tangerine
Dragon
Oct 2012

39. DeepLanguageUnderstanding
Symbolic methods complement machine learning in a common architecture
Amount of domain-specific data
Accuracy
Combined
Symbolic-only
Data only

40. + TOY BRIDGES ?…
Categorical Logic, Dialectica
Categories and Their Applications
Automated Theorem Proving and
Semantics of Programming Languages
Linear Functional Programming,
Abstract Machines and Modal Type
Theories
Logics for NLP, for Linguistic Inference
and for Contexts in AI
Combining symbolic methods and
analytics to solve big data problems

41. +
Are we there yet?
Working in interdisciplinary areas is hard,
but rewarding.
n The frontier between logic, computing,
linguistics and categories is a fun place
to be.
n Mathematics teaches you a way of
thinking, more than specific theorems.
n Barriers: proprietary software and
unwillingness to `waste time’ on
formalizations
n Enablers: international scientific
communities, open access NLP and
other software, growing interaction
between fields,…
n Handsome payoff expected…
n Fall in love with your ideas and enjoy
talking to many about them...

42. +
Thanks!

43. +
Women in Logic
Tomorrow!
What
about
issues?

44. +
WiL2017

45. +

46. +Some references
n Godel's Collected Works, eds Feferman and Dawson
n Full Intuitionistic Linear Logic (extended abstract). (with Martin Hyland). Annals of Pure
and Applied Logic, 64(3), pp.273-291, 1993. pdf
n Valeria de Paiva. Bridges from Language to Logic: Concepts,
Contexts and Ontologies. ENTCS, 22 April 2011. Proceedings of
the Fifth Logical and Semantic Frameworks, with Applications
Workshop (LSFA 2010). [PDF]
n Recent publications from http://vcvpaiva.github.io/pubs.html
n Older publications from
http://www.cs.bham.ac.uk/~vdp/publications/papers.html
n Google Scholar
https://scholar.google.com/citations?user=AYdo1hMAAAAJ&hl=en

47. +
Thanks!