+

Weapons of Math Construction: Proofs for Programs and Personal Assistants

Valeria de PaivaNuance Communications, Sunnyvale, CA

+What a title!

+Minas Gerais, Brazil

Personal and inspiring?

+PUC—Rio de Janeiro Maths Dept

+University of CambridgePure Maths (old DPMMS)

+University of CambridgePure Maths (old DPMMS)

+University of CambridgePure Maths (DPMMS)

Dialectica Categories PhD thesisGödel: consistency of Arithmetic.Internal categorical model Dialectica!

(very precise) models of Linear Logic.

+ University of Cambridge

+University of CambridgeComputer Laboratory1989-1995

Formalizing and proving about automated reasoning:subtyping and dependent typesAcquisition of Lexical Semantics, Machine Readable Dictionaries, AcquilexConstructive Modal Logic and properties of programsAuthentication and authorization logics

+University of Birmingham, UKComputer Science - professor

+Birmingham & xSLAM project

Explicit SubstitutionsLinear functional ProgrammingConstructive NecessityIntuitionistic and Linear CalculusFull Intuitionistic Linear Logic Constructive Hybrid Logic, etc

+ NLTT: Natural Language Theory and TechnologyOctober 2000-May 2008

+ NLTT: Natural Language Theory and Technology1999-2008

KXDC (Knowledge eXtraction from Document Collections)NIMD (Novel Intelligence from Massive Data)AQUAINT (Advanced Question Answering from Text)

+PowerSet and Spin Outs

+NLTT: Natural Language Theory and Technology

n Spinning out technology is a tradition

n Split out the group

n Take a plunge!

+Adventures in SearchlandPARC Forum

n Valeria de Paiva, Cuil, Search Analyst

n 30 July 20094:00-5:00pmGeorge E. Pake Auditorium, PARC, Palo Alto, CAmap/ directions

n http://www.parc.com/event/934/adventures-in-searchland.html

n Video and audio

+Launching a hotproduct…

+After the hype, the blogsphere….

+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..

+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 as Yahoo shows, the barrier is every time higher…

+The Financial Crisis

+Rearden Commerce? ...

+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?

+Nuance Comms,AI and NL Lab, Sunnyvale, CA

2012-now

+The Future is Meaning…

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

+Curry-Howard Correspondence Triangles

Lambda-calculus

IntuitionisticPropositional

Logic

Cartesian Closed

Categories1963 1965

+How do I get into this picture?

+Same triangle...different logicLinear Logic, a proof theoretic logic

described by Jean-Yves Girard in 1986.

Basic idea: assumptions cannot bediscarded or duplicated. They mustbe used exactly once—just like dollarbills...

Other approaches to accounting forlogical 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

+Curry-Howard Correspondence

Linear Lambda-Calculus

Linear Logic

Linear Categories

+Curry-Howard Correspondence TriangleS

Functional Programming

Proof TheoryCategory Theory

How many? Which applications? Reactive Functional programming? Android apps race conditions? Rust and effect calculus?

+My example: Dialectica categories

Linear Lambda Calculus

(Int) Linear Logic

DialecticaCategories

+(many )More Dialectica CategoriesModels 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

+Bridges?

Tran

slat

ion

+The Future is Meaning

http://www.wired.com/2013/03/conversational-user-interface/

SiriOct 2011

Google NowJul 2012

NinaAug 2012

USAA EVA

CVS

CortanaAug 2014

DomOct 2014

USAA CoachMay 2015

Voice based Virtual Assistants pavingthe way for general acceptance of AI

INGE

LilyMay 2013

Tangerine

DragonOct 2012

Deep Language UnderstandingSymbolic methods complement machine learning in a common architecture

Amount of domain-specific data

Accuracy

Combined

Symbolic-only

Data only

+ TOY BRIDGES ?…

Categorical Logic, DialecticaCategories 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

+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...

+

Thanks!

+

Women in LogicTomorrow!

What about

issues?

+WiL2017

+

+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 ofthe Fifth Logical and Semantic Frameworks, with ApplicationsWorkshop (LSFA 2010). [PDF]

n Recent publications from http://vcvpaiva.github.io/pubs.html

n Older publications fromhttp://www.cs.bham.ac.uk/~vdp/publications/papers.html

n Google Scholar https://scholar.google.com/citations?user=AYdo1hMAAAAJ&hl=en

+Thanks!