Conexus - Category Theory for Semantic Data Interoperability

Category Theory for Semantic Data InteroperabilityExchange and Consolidate Data for Agile PLM at Scale

San Francisco | New York City | Boston | Munich 2

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Data Integration Challenges


<<requirement>>Climb: One-engine-inoperative

FEDERAL AVIATION ADMINISTRATION (FAA) Title 14, Chapter 1, Subchapter C 25.121

…(a) Takeoff; landing gear extended… the steady gradient of column… not less than 0.5 percent… for four-engine airplanes

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© 2021 Conexus AI, Inc.






Perform simulation under conditions...

<<testcase>>Climb: One-engine-inoperativeTest Case

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~N2Data Integration Challenges

San Francisco | New York City | Boston | Munich



San Francisco | New York City | Boston | Munich 23Adapted from Breiner, S, Applied Category Theory workshop, National Institute Standards and Technology, 2017

Variety of Source Systems

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Trying to standardize semantics globally sacrifice domain-specific semantic fidelity.



San Francisco | New York City | Boston | Munich 33Adapted from Breiner, S, Applied Category Theory workshop, National Institute Standards and Technology, 2017

Sacrifice domain-specific semantic fidelity. VS


Semantic Data InteroperabilityEnabled by Categorical Mathematics

Category Theory History


1890-1945 Foundational Ideas

Ideas leading to categories, functors,

and natural transformations

2011 OlogsDiscovery connecting categories to

database/ontology schemas

2019 Algebraic Property Graphs

APG published as an interoperable

enterprise knowledge graph meta-model

Uber u

ses A

CT to i

ntero

pera

te hu

ndre

ds

of tho

usan

ds of

data

sour

ces

2019

-Now

Ube

r Int

erop

erab

ility

Multipl

e pro

jects

launc

hing t

o

utiliz

e ACT t

o driv

e

engin

eerin

g sys

tem

inter

oper

abilit

y

Now

2018 Applied Category Theory

Applied Category Theory (ACT) expanded

more broadly to semantic IT interoperability

Applie

d Cate

gory

Theo

ry (A

CT) ut

ilized

commer

cially

acro

ss va

rious

indu

stries

to int

egra

te da

ta

2011

-2015

Vario

us A

pplic

ation

s

Catego

ry Th

eory

deve

loped

over

deca

des i

nto a

comple

te the

ory

1945

-1970

Ear

ly Dev

elopm

ent

1971 Categories for Working

Mathematician Published

Standard reference for Category

Theory

Dozen

s of c

ontrib

ution

s mad

e to f

urthe

r

deve

lop an

d exp

and C

atego

ry Th

eory

1971

-2011

Late

Develo

pmen

t


Category Theory History



David Spivak Ryan WisneskyMIT MIT

Foundationally Better Cost Scaling


Variety of Source Systems

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4 v 6




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8 v 20




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New Data Integration Paradigm







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Required Inputs

● Data Schema● Data Records● Schema Links (as schema)● Record Links (as records)● Rules (declarative)

Automatically Compose Data Sources



Automatically Compose Data Sources


Data, Concepts, Relationships & Rules AKA Records, Attributes, References & Constraints


Exploiting Categorical Mathematics

● Automate composition of integrations● Merge data models, schemas and ontologies safely● Exchange and consolidate data● Enable forward and backward compatibility● Curate and add sources incrementally● Enforce global and domain-specific rules● Machine-verify integrity of integrations● Quantify implications of imperfect integrations● Interoperate between any kind of data structure

Conexus Enables New Paradigm



Semantic Fabric



Semantic Fabric



Semantic Data InteroperabilityEnabled by Categorical Mathematics

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Conexus - Category Theory for Semantic Data Interoperability