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Weapons of Math Construction


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Talk at the Logic Mentoring Workshop, LiCS 2017

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Weapons of Math Construction

  1. 1. + Weapons of Math Construction: Proofs for Programs and Personal Assistants Valeria de Paiva Nuance Communications, Sunnyvale, CA
  2. 2. + What a title!
  3. 3. + Minas Gerais, Brazil Personal and inspiring?
  4. 4. + PUC—Rio de Janeiro Maths Dept
  5. 5. + University of Cambridge Pure Maths (old DPMMS)
  6. 6. + University of Cambridge Pure Maths (old DPMMS)
  7. 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. 8. +University of Cambridge
  9. 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. 10. + University of Birmingham, UK Computer Science - professor
  11. 11. + Birmingham & xSLAM project Explicit Substitutions Linear functional Programming Constructive Necessity Intuitionistic and Linear Calculus Full Intuitionistic Linear Logic Constructive Hybrid Logic, etc
  12. 12. + NLTT: Natural Language Theory and Technology October 2000-May 2008
  13. 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. 14. + PowerSet and Spin Outs
  15. 15. + NLTT: Natural Language Theory and Technology n Spinning out technology is a tradition n Split out the group n Take a plunge!
  16. 16. + 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 34/adventures-in- searchland.html n Video and audio
  17. 17. + Launching a hot product…
  18. 18. + After the hype, the blogsphere….
  19. 19. +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..
  20. 20. +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, But asYahoo shows, the barrier is every time higher…
  21. 21. + The Financial Crisis
  22. 22. + Rearden Commerce? ...
  23. 23. + 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?
  24. 24. + Nuance Comms, AI and NL Lab, Sunnyvale, CA 2012-now
  25. 25. + The Future is Meaning…
  26. 26. + Unity Behind Disparity: Proofs are Programs?...
  27. 27. + Curry-Howard Correspondence Triangles Lambda- calculus Intuitionistic Propositional Logic Cartesian Closed Categories 1963 1965
  28. 28. +How do I get into this picture?
  29. 29. +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
  30. 30. + Curry-Howard Correspondence Linear Lambda- Calculus Linear Logic Linear Categories
  31. 31. + 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?
  32. 32. +My example: Dialectica categories Linear Lambda Calculus (Int) Linear Logic Dialectica Categories
  33. 33. +(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
  34. 34. + Bridges? Translation
  35. 35. + The Future is Meaning
  36. 36. 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
  37. 37. DeepLanguageUnderstanding Symbolic methods complement machine learning in a common architecture Amount of domain-specific data Accuracy Combined Symbolic-only Data only
  38. 38. + 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
  39. 39. + 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...
  40. 40. + Thanks!
  41. 41. + Women in Logic Tomorrow! What about issues?
  42. 42. + WiL2017
  43. 43. +
  44. 44. +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 n Older publications from n Google Scholar
  45. 45. + Thanks!