conexus - category theory for semantic data interoperability
TRANSCRIPT
Category Theory for Semantic Data InteroperabilityExchange and Consolidate Data for Agile PLM at Scale
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© 2021 Conexus AI, Inc. – Confidential document.
Data Integration Challenges
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<<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
Requirement
© 2021 Conexus AI, Inc.
Data Integration Challenges
San Francisco | New York City | Boston | Munich 4
<<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
Perform simulation under conditions...
<<testcase>>Climb: One-engine-inoperativeTest Case
Requirement
© 2021 Conexus AI, Inc.
Data Integration Challenges
San Francisco | New York City | Boston | Munich 5
<<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
Perform simulation under conditions...
<<testcase>>Climb: One-engine-inoperativeTest Case
RequirementDesign
© 2021 Conexus AI, Inc.
Data Integration Challenges
San Francisco | New York City | Boston | Munich 6
<<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
Perform simulation under conditions...
<<testcase>>Climb: One-engine-inoperativeTest Case
Requirement
Simulation
Design
© 2021 Conexus AI, Inc.
Data Integration Challenges
San Francisco | New York City | Boston | Munich 7
<<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
Perform simulation under conditions...
<<testcase>>Climb: One-engine-inoperativeTest Case
Requirement
Simulation
Design
Manufacturing Process Planning
© 2021 Conexus AI, Inc.
Data Integration Challenges
San Francisco | New York City | Boston | Munich 8
<<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
Perform simulation under conditions...
<<testcase>>Climb: One-engine-inoperativeTest Case
Requirement
Simulation
Design
Control System Logic
Manufacturing Process Planning
© 2021 Conexus AI, Inc.
Data Integration Challenges
San Francisco | New York City | Boston | Munich 9
<<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
Perform simulation under conditions...
<<testcase>>Climb: One-engine-inoperativeTest Case
Requirement
Simulation
Design
Control System Logic
Manufacturing Process Planning
Bill of Materials
© 2021 Conexus AI, Inc.
Data Integration Challenges
San Francisco | New York City | Boston | Munich 10
Design
© 2021 Conexus AI, Inc.
Data Integration Challenges
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© 2021 Conexus AI, Inc.
Data Integration Challenges
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© 2021 Conexus AI, Inc.
Data Integration Challenges
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© 2021 Conexus AI, Inc.
Data Integration Challenges
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v2
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~N2Data Integration Challenges
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Data Integration Challenges
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
Costs
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Data Integration Challenges
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© 2021 Conexus AI, Inc.
Data Integration Challenges
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© 2021 Conexus AI, Inc.
Data Integration Challenges
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© 2021 Conexus AI, Inc.
Data Integration Challenges
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© 2021 Conexus AI, Inc.
Data Integration Challenges
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© 2021 Conexus AI, Inc.
Data Integration Challenges
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??
© 2021 Conexus AI, Inc.
Data Integration Challenges
San Francisco | New York City | Boston | Munich 30
<<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
Perform simulation under conditions...
<<testcase>>Climb: One-engine-inoperativeTest Case
Requirement
Simulation
Design
Control System Logic
Manufacturing Process Planning
Bill of Materials
© 2021 Conexus AI, Inc.
Data Integration Challenges
San Francisco | New York City | Boston | Munich
© 2021 Conexus AI, Inc.
Data Integration Challenges
San Francisco | New York City | Boston | Munich 32
<<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
Perform simulation under conditions...
<<testcase>>Climb: One-engine-inoperativeTest Case
Requirement
Simulation
Design
Control System Logic
Manufacturing Process Planning
Bill of Materials
Trying to standardize semantics globally sacrifice domain-specific semantic fidelity.
© 2021 Conexus AI, Inc.
Data Integration Challenges
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
© 2021 Conexus AI, Inc.
Semantic Data InteroperabilityEnabled by Categorical Mathematics
Category Theory History
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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
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Category Theory History
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© 2021 Conexus AI, Inc.
David Spivak Ryan WisneskyMIT MIT
Foundationally Better Cost Scaling
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Variety of Source Systems
Costs
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Foundationally Better Cost Scaling
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v2
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v2
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Foundationally Better Cost Scaling
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v2
© 2021 Conexus AI, Inc.
New Data Integration Paradigm
San Francisco | New York City | Boston | Munich 51
<<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
Perform simulation under conditions...
<<testcase>>Climb: One-engine-inoperativeTest Case
Requirement
Simulation
Design
Control System Logic
Manufacturing Process Planning
Bill of Materials
© 2021 Conexus AI, Inc.
New Data Integration Paradigm
San Francisco | New York City | Boston | Munich 52
© 2021 Conexus AI, Inc.
New Data Integration Paradigm
San Francisco | New York City | Boston | Munich 53
© 2021 Conexus AI, Inc.
New Data Integration Paradigm
San Francisco | New York City | Boston | Munich 54
© 2021 Conexus AI, Inc.
New Data Integration Paradigm
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© 2021 Conexus AI, Inc.
New Data Integration Paradigm
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© 2021 Conexus AI, Inc.
New Data Integration Paradigm
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© 2021 Conexus AI, Inc.
Required Inputs
● Data Schema● Data Records● Schema Links (as schema)● Record Links (as records)● Rules (declarative)
Automatically Compose Data Sources
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© 2021 Conexus AI, Inc.
Automatically Compose Data Sources
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Data, Concepts, Relationships & Rules AKA Records, Attributes, References & Constraints
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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
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Semantic Fabric
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© 2021 Conexus AI, Inc. – Confidential document.
Semantic Fabric
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© 2021 Conexus AI, Inc. – Confidential document.
Semantic Data InteroperabilityEnabled by Categorical Mathematics