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Weapons of Math Construction: Proofs for Programs and Personal Assistants
Valeria de PaivaNuance Communications, Sunnyvale, CA
+University of CambridgePure Maths (DPMMS)
Dialectica Categories PhD thesisGödel: consistency of Arithmetic.Internal categorical model Dialectica!
(very precise) models of Linear Logic.
+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
+Birmingham & xSLAM project
Explicit SubstitutionsLinear functional ProgrammingConstructive NecessityIntuitionistic and Linear CalculusFull Intuitionistic Linear Logic Constructive Hybrid Logic, etc
+ 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)
+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
+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…
+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?
+Curry-Howard Correspondence Triangles
Lambda-calculus
IntuitionisticPropositional
Logic
Cartesian Closed
Categories1963 1965
+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 TriangleS
Functional Programming
Proof TheoryCategory Theory
How many? Which applications? Reactive Functional programming? Android apps race conditions? Rust and effect calculus?
+(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
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...
+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
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