agreeing to disagree: reconciling conflicting taxonomic views using a logic-based approach
TRANSCRIPT
Agreeing to disagree: Reconciling Conflicting Taxonomic Views
using a Logic-based Approach
Yi-Yun (Jessica) Cheng, Nico Franz, Jodi SchneiderShizhuo Yu, Thomas Rodenhausen, Bertram Ludäscher
[email protected] https://github.com/EulerProject/ASIST17
Tina and Amy meet at the water cooler …
Tina:HeyAmy,canyourecommendasignaturedishfromwhereyoulive?
Amy:Oh,definitelythehalf-smokes fromthe Northeast!Theyarethesetastyhalf-porkandhalf-beefsausages.
Tina:Whatacoincidence!Wehavehalf-smokesinthe South,too!WheredoyouliveintheNortheast?NewYork?Boston?
Amy:Wrongguesses!WheredoyouliveintheSouth?
TinaandAmytogether:Washington,D.C.
[Thetwoofthemlookateachother,confused.]
11/01/17 Cheng
Two Taxonomies
“…in the face of incompatible information or data structures among users or among thosespecifying the system, attempts to create unitary knowledge categories are futile. Rather,parallel or multiple representational forms are required” [Bowker & Star, 2000, p.159]
11/01/17 Cheng
West
Southwest Southeast
Midwest North-east
West
South
Midwest North-east
NationalDiversityCouncilmap(NDC) USCensusBuero map(CEN)
The taxonomies
11/01/17 Cheng
• The Census Regions Map (CEN), consists of fourregions: West, Midwest, Northeast, and South, i.e., the contiguous 48 states and Washington D.C.
West
South
Midwest
North-east
The taxonomies
11/01/17 Cheng
• The National Diversity Council Map (NDC), consists of five regions: West, Southwest, Midwest, Northeast, Southeast, the 48 states and Washington D.C.
NDC(withstates)
West
Southwest Southeast
Midwest North-east
• NDC splits South into SW and SE
• Do NDC and CEN agree on “West”? “Midwest”? …
• How can we sort this out?
Sorting things out …
11/01/17 Cheng
CEN.Midwest
CEN.USA
CEN.South CEN.West CEN.Northeast NDC.Northeast
NDC.USA
NDC.Southeast NDC.Midwest NDC.Southwest NDC.West
Nodes
CEN 5NDC 6 Edges
is_a (CEN) 4is_a (NDC) 5
CEN.South
NDC.Northeast
o
NDC.Southwest
o
NDC.Southeast>
CEN.Midwest NDC.Midwest=
CEN.USA
CEN.West
CEN.NortheastNDC.USA
=
!
oNDC.West
>
<
Nodes
CEN 5NDC 6 Edges
is_a (CEN) 4is_a (NDC) 5articulations 9
CEN.Midwest
CEN.USA
CEN.South CEN.West CEN.Northeast NDC.Northeast
NDC.USA
NDC.Southeast NDC.Midwest NDC.Southwest NDC.West
Nodes
CEN 5NDC 6 Edges
is_a (CEN) 4is_a (NDC) 5
• Given:– taxonomies T1, T2– and relations T1 ~ T2
(articulations, alignment) • Find:
– merged taxonomy T3 • Such that:
– T1, T2 are preserved– all pairwise relations are
explicit
T1 T2
5 ways to relate concepts (regions)
• Idea: relate concepts X and Y with articulations
• Articulation Language: Region Connection Calculus (RCC5): congruence, inclusion, inverse inclusion, overlap, disjointness
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Y X X YX Y X Y X Y
CongruenceX == Y
InclusionX > Y
Inverse InclusionX < Y
OverlapX>< Y
DisjointnessX ! Y
CEN.South
NDC.Northeast
><
NDC.Southwest
><
NDC.Southeast>
CEN.Midwest NDC.Midwest==
CEN.USA
CEN.West
CEN.NortheastNDC.USA
==
!
><NDC.West
>
<
Nodes
CEN 5NDC 6 Edges
is_a (CEN) 4is_a (NDC) 5articulations 9
Merged taxonomy T3
11/01/17 Cheng
CEN.South
NDC.Northeast
NDC.Southwest
CEN.USANDC.USA
CEN.West
CEN.Northeast
NDC.Southeast
NDC.West
CEN.MidwestNDC.Midwest
Nodes
CEN 3NDC 4
congruent 2 Edges
is_a (input) 8overlaps (input) 3
CEN.Midwest
CEN.USA
CEN.South CEN.West CEN.Northeast NDC.Northeast
NDC.USA
NDC.Southeast NDC.Midwest NDC.Southwest NDC.West
Nodes
CEN 5NDC 6 Edges
is_a (CEN) 4is_a (NDC) 5
CEN.Midwest
CEN.USA
CEN.South CEN.West CEN.Northeast NDC.Northeast
NDC.USA
NDC.Southeast NDC.Midwest NDC.Southwest NDC.West
Nodes
CEN 5NDC 6 Edges
is_a (CEN) 4is_a (NDC) 5
CEN.South
NDC.Northeast
><
NDC.Southwest
><
NDC.Southeast>
CEN.Midwest NDC.Midwest==
CEN.USA
CEN.West
CEN.NortheastNDC.USA
==
!
><NDC.West
>
<
Nodes
CEN 5NDC 6 Edges
is_a (CEN) 4is_a (NDC) 5articulations 9
T1 T2
T1~T2 T3
How we align two taxonomies T1 and T2
• Step 1. Supply input taxonomies T1 and T2
• Step 2. Describe the relationships between T1 and T2
• Step 3. Iteratively edit articulations in Euler/X
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T1 T2
T1 T2
Inconsistent (N=0) Ambiguous (N>1)
T3
Add/Edit Articulations A
Euler/X
N Possible Worlds
N=1 N=0 or N>1
• … but where do the articulationscome from??– expert opinion– automatically derived from data
Case 1. Census Region vs. National Diversity Council
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West
South
Midwest
North-east
NDC(withstates)
West
Southwest Southeast
Midwest North-east
CEN NDC
• … but where do the articulationscome from??– automatically derived from data– expert opinion
11/01/17 Cheng
CEN.IL NDC.IL==
CEN.IN NDC.IN==
CEN.RI NDC.RI==
CEN.IA NDC.IA==
CEN.WV NDC.WV==
CEN.KS NDC.KS==
CEN.KY NDC.KY==
CEN.TX NDC.TX==
CEN.NortheastCEN.VTCEN.MA
CEN.ME
CEN.CT
CEN.PA
CEN.NY
CEN.NH
CEN.NJ
CEN.South
CEN.TN
CEN.MS
CEN.MD
CEN.DC
CEN.DE
CEN.VA
CEN.FL
CEN.AR
CEN.AL
CEN.OK
CEN.SC
CEN.LACEN.GA
CEN.NC
CEN.ID NDC.ID==
NDC.TN==
CEN.WY NDC.WY==
NDC.VT==
NDC.MS==
CEN.MT NDC.MT==
NDC.MA==
CEN.USA
CEN.Midwest
CEN.West
NDC.ME==
NDC.MD==
CEN.MI NDC.MI==
CEN.MN NDC.MN==
NDC.DC==
NDC.DE==
CEN.OR NDC.OR==
CEN.OH NDC.OH==
NDC.VA==
NDC.FL==
NDC.AR==
CEN.AZ NDC.AZ==
NDC.AL==
NDC.OK==
NDC.CT==
CEN.CO NDC.CO==
CEN.CA NDC.CA==
CEN.SD NDC.SD==
NDC.SC==
CEN.MO
CEN.ND
CEN.NE
CEN.WI
NDC.LA==
NDC.MO==
CEN.UT NDC.UT==
NDC.GA==
NDC.PA==
CEN.NV
CEN.NM
CEN.WA
NDC.NY==
NDC.NV==
NDC.NM==
NDC.WA==
NDC.NH==
NDC.NJ==
NDC.ND==
NDC.NE==
NDC.WI==
NDC.NC==
NDC.West
NDC.Midwest
NDC.Northeast
NDC.Southeast
NDC.USA
NDC.Southwest
Nodes
CEN 54NDC 55 Edges
isa_CEN 53isa_NDC 54Art. 49
CEN.IL NDC.IL==
CEN.IN NDC.IN==
CEN.RI NDC.RI==
CEN.IA NDC.IA==
CEN.WV NDC.WV==
CEN.KS NDC.KS==
CEN.KY NDC.KY==
CEN.TX NDC.TX==
CEN.NortheastCEN.VTCEN.MA
CEN.ME
CEN.CT
CEN.PA
CEN.NY
CEN.NH
CEN.NJ
CEN.South
CEN.TN
CEN.MS
CEN.MD
CEN.DC
CEN.DE
CEN.VA
CEN.FL
CEN.AR
CEN.AL
CEN.OK
CEN.SC
CEN.LACEN.GA
CEN.NC
CEN.ID NDC.ID==
NDC.TN==
CEN.WY NDC.WY==
NDC.VT==
NDC.MS==
CEN.MT NDC.MT==
NDC.MA==
CEN.USA
CEN.Midwest
CEN.West
NDC.ME==
NDC.MD==
CEN.MI NDC.MI==
CEN.MN NDC.MN==
NDC.DC==
NDC.DE==
CEN.OR NDC.OR==
CEN.OH NDC.OH==
NDC.VA==
NDC.FL==
NDC.AR==
CEN.AZ NDC.AZ==
NDC.AL==
NDC.OK==
NDC.CT==
CEN.CO NDC.CO==
CEN.CA NDC.CA==
CEN.SD NDC.SD==
NDC.SC==
CEN.MO
CEN.ND
CEN.NE
CEN.WI
NDC.LA==
NDC.MO==
CEN.UT NDC.UT==
NDC.GA==
NDC.PA==
CEN.NV
CEN.NM
CEN.WA
NDC.NY==
NDC.NV==
NDC.NM==
NDC.WA==
NDC.NH==
NDC.NJ==
NDC.ND==
NDC.NE==
NDC.WI==
NDC.NC==
NDC.West
NDC.Midwest
NDC.Northeast
NDC.Southeast
NDC.USA
NDC.Southwest
Nodes
CEN 54NDC 55 Edges
isa_CEN 53isa_NDC 54Art. 49
11/01/17 Cheng
CEN.West
NDC.Southwest
CEN.USANDC.USA
CEN.Northeast
NDC.Northeast
CEN.SouthNDC.Southeast
NDC.West
CEN.DCNDC.DC
CEN.NMNDC.NM
CEN.NDNDC.ND
CEN.MidwestNDC.Midwest
CEN.AZNDC.AZ
CEN.CANDC.CA
CEN.MTNDC.MT
CEN.MANDC.MA
CEN.INNDC.IN
CEN.NVNDC.NV
CEN.MDNDC.MD
CEN.CTNDC.CT
CEN.NHNDC.NH
CEN.KYNDC.KY
CEN.PANDC.PA
CEN.CONDC.CO
CEN.WANDC.WA
CEN.MINDC.MI
CEN.VANDC.VA
CEN.WINDC.WI
CEN.NENDC.NE
CEN.SDNDC.SD
CEN.MNNDC.MN
CEN.MSNDC.MS
CEN.IDNDC.ID
CEN.WVNDC.WV
CEN.NYNDC.NY
CEN.NJNDC.NJ
CEN.UTNDC.UT
CEN.MENDC.ME
CEN.ILNDC.IL
CEN.TNNDC.TN
CEN.VTNDC.VT
CEN.GANDC.GA
CEN.DENDC.DE
CEN.NCNDC.NC
CEN.OKNDC.OK
CEN.MONDC.MO
CEN.SCNDC.SC
CEN.ARNDC.AR
CEN.TXNDC.TX
CEN.LANDC.LA
CEN.OHNDC.OH
CEN.IANDC.IA
CEN.KSNDC.KS
CEN.RINDC.RI
CEN.WYNDC.WY
CEN.FLNDC.FL
CEN.ORNDC.OR
CEN.ALNDC.AL
Nodes
CEN 3NDC 4comb 51 Edges
input 61inferred 3
overlapsinferred 3
CEN.West
NDC.Southwest
CEN.USANDC.USA
CEN.Northeast
NDC.Northeast
CEN.SouthNDC.Southeast
NDC.West
CEN.DCNDC.DC
CEN.NMNDC.NM
CEN.NDNDC.ND
CEN.MidwestNDC.Midwest
CEN.AZNDC.AZ
CEN.CANDC.CA
CEN.MTNDC.MT
CEN.MANDC.MA
CEN.INNDC.IN
CEN.NVNDC.NV
CEN.MDNDC.MD
CEN.CTNDC.CT
CEN.NHNDC.NH
CEN.KYNDC.KY
CEN.PANDC.PA
CEN.CONDC.CO
CEN.WANDC.WA
CEN.MINDC.MI
CEN.VANDC.VA
CEN.WINDC.WI
CEN.NENDC.NE
CEN.SDNDC.SD
CEN.MNNDC.MN
CEN.MSNDC.MS
CEN.IDNDC.ID
CEN.WVNDC.WV
CEN.NYNDC.NY
CEN.NJNDC.NJ
CEN.UTNDC.UT
CEN.MENDC.ME
CEN.ILNDC.IL
CEN.TNNDC.TN
CEN.VTNDC.VT
CEN.GANDC.GA
CEN.DENDC.DE
CEN.NCNDC.NC
CEN.OKNDC.OK
CEN.MONDC.MO
CEN.SCNDC.SC
CEN.ARNDC.AR
CEN.TXNDC.TX
CEN.LANDC.LA
CEN.OHNDC.OH
CEN.IANDC.IA
CEN.KSNDC.KS
CEN.RINDC.RI
CEN.WYNDC.WY
CEN.FLNDC.FL
CEN.ORNDC.OR
CEN.ALNDC.AL
Nodes
CEN 3NDC 4comb 51 Edges
input 61inferred 3
overlapsinferred 3
USA,MidwestandState-levelalignmentsareallcongruent
11/01/17 Cheng
CEN.West
NDC.Southwest
CEN.USANDC.USA
CEN.Northeast
NDC.Northeast
CEN.SouthNDC.Southeast
NDC.West
CEN.DCNDC.DC
CEN.NMNDC.NM
CEN.NDNDC.ND
CEN.MidwestNDC.Midwest
CEN.AZNDC.AZ
CEN.CANDC.CA
CEN.MTNDC.MT
CEN.MANDC.MA
CEN.INNDC.IN
CEN.NVNDC.NV
CEN.MDNDC.MD
CEN.CTNDC.CT
CEN.NHNDC.NH
CEN.KYNDC.KY
CEN.PANDC.PA
CEN.CONDC.CO
CEN.WANDC.WA
CEN.MINDC.MI
CEN.VANDC.VA
CEN.WINDC.WI
CEN.NENDC.NE
CEN.SDNDC.SD
CEN.MNNDC.MN
CEN.MSNDC.MS
CEN.IDNDC.ID
CEN.WVNDC.WV
CEN.NYNDC.NY
CEN.NJNDC.NJ
CEN.UTNDC.UT
CEN.MENDC.ME
CEN.ILNDC.IL
CEN.TNNDC.TN
CEN.VTNDC.VT
CEN.GANDC.GA
CEN.DENDC.DE
CEN.NCNDC.NC
CEN.OKNDC.OK
CEN.MONDC.MO
CEN.SCNDC.SC
CEN.ARNDC.AR
CEN.TXNDC.TX
CEN.LANDC.LA
CEN.OHNDC.OH
CEN.IANDC.IA
CEN.KSNDC.KS
CEN.RINDC.RI
CEN.WYNDC.WY
CEN.FLNDC.FL
CEN.ORNDC.OR
CEN.ALNDC.AL
Nodes
CEN 3NDC 4comb 51 Edges
input 61inferred 3
overlapsinferred 3
CEN.West
NDC.Southwest
CEN.USANDC.USA
CEN.Northeast
NDC.Northeast
CEN.SouthNDC.Southeast
NDC.West
CEN.DCNDC.DC
CEN.NMNDC.NM
CEN.NDNDC.ND
CEN.MidwestNDC.Midwest
CEN.AZNDC.AZ
CEN.CANDC.CA
CEN.MTNDC.MT
CEN.MANDC.MA
CEN.INNDC.IN
CEN.NVNDC.NV
CEN.MDNDC.MD
CEN.CTNDC.CT
CEN.NHNDC.NH
CEN.KYNDC.KY
CEN.PANDC.PA
CEN.CONDC.CO
CEN.WANDC.WA
CEN.MINDC.MI
CEN.VANDC.VA
CEN.WINDC.WI
CEN.NENDC.NE
CEN.SDNDC.SD
CEN.MNNDC.MN
CEN.MSNDC.MS
CEN.IDNDC.ID
CEN.WVNDC.WV
CEN.NYNDC.NY
CEN.NJNDC.NJ
CEN.UTNDC.UT
CEN.MENDC.ME
CEN.ILNDC.IL
CEN.TNNDC.TN
CEN.VTNDC.VT
CEN.GANDC.GA
CEN.DENDC.DE
CEN.NCNDC.NC
CEN.OKNDC.OK
CEN.MONDC.MO
CEN.SCNDC.SC
CEN.ARNDC.AR
CEN.TXNDC.TX
CEN.LANDC.LA
CEN.OHNDC.OH
CEN.IANDC.IA
CEN.KSNDC.KS
CEN.RINDC.RI
CEN.WYNDC.WY
CEN.FLNDC.FL
CEN.ORNDC.OR
CEN.ALNDC.AL
Nodes
CEN 3NDC 4comb 51 Edges
input 61inferred 3
overlapsinferred 3
Theoverlappingrelationsareautomaticallyderivedfromdata
11/01/17 Cheng
CEN.West
NDC.Southwest
CEN.USANDC.USA
CEN.Northeast
NDC.Northeast
CEN.SouthNDC.Southeast
NDC.West
CEN.DCNDC.DC
CEN.NMNDC.NM
CEN.NDNDC.ND
CEN.MidwestNDC.Midwest
CEN.AZNDC.AZ
CEN.CANDC.CA
CEN.MTNDC.MT
CEN.MANDC.MA
CEN.INNDC.IN
CEN.NVNDC.NV
CEN.MDNDC.MD
CEN.CTNDC.CT
CEN.NHNDC.NH
CEN.KYNDC.KY
CEN.PANDC.PA
CEN.CONDC.CO
CEN.WANDC.WA
CEN.MINDC.MI
CEN.VANDC.VA
CEN.WINDC.WI
CEN.NENDC.NE
CEN.SDNDC.SD
CEN.MNNDC.MN
CEN.MSNDC.MS
CEN.IDNDC.ID
CEN.WVNDC.WV
CEN.NYNDC.NY
CEN.NJNDC.NJ
CEN.UTNDC.UT
CEN.MENDC.ME
CEN.ILNDC.IL
CEN.TNNDC.TN
CEN.VTNDC.VT
CEN.GANDC.GA
CEN.DENDC.DE
CEN.NCNDC.NC
CEN.OKNDC.OK
CEN.MONDC.MO
CEN.SCNDC.SC
CEN.ARNDC.AR
CEN.TXNDC.TX
CEN.LANDC.LA
CEN.OHNDC.OH
CEN.IANDC.IA
CEN.KSNDC.KS
CEN.RINDC.RI
CEN.WYNDC.WY
CEN.FLNDC.FL
CEN.ORNDC.OR
CEN.ALNDC.AL
Nodes
CEN 3NDC 4comb 51 Edges
input 61inferred 3
overlapsinferred 3
CEN.West
NDC.Southwest
CEN.USANDC.USA
CEN.Northeast
NDC.Northeast
CEN.SouthNDC.Southeast
NDC.West
CEN.DCNDC.DC
CEN.NMNDC.NM
CEN.NDNDC.ND
CEN.MidwestNDC.Midwest
CEN.AZNDC.AZ
CEN.CANDC.CA
CEN.MTNDC.MT
CEN.MANDC.MA
CEN.INNDC.IN
CEN.NVNDC.NV
CEN.MDNDC.MD
CEN.CTNDC.CT
CEN.NHNDC.NH
CEN.KYNDC.KY
CEN.PANDC.PA
CEN.CONDC.CO
CEN.WANDC.WA
CEN.MINDC.MI
CEN.VANDC.VA
CEN.WINDC.WI
CEN.NENDC.NE
CEN.SDNDC.SD
CEN.MNNDC.MN
CEN.MSNDC.MS
CEN.IDNDC.ID
CEN.WVNDC.WV
CEN.NYNDC.NY
CEN.NJNDC.NJ
CEN.UTNDC.UT
CEN.MENDC.ME
CEN.ILNDC.IL
CEN.TNNDC.TN
CEN.VTNDC.VT
CEN.GANDC.GA
CEN.DENDC.DE
CEN.NCNDC.NC
CEN.OKNDC.OK
CEN.MONDC.MO
CEN.SCNDC.SC
CEN.ARNDC.AR
CEN.TXNDC.TX
CEN.LANDC.LA
CEN.OHNDC.OH
CEN.IANDC.IA
CEN.KSNDC.KS
CEN.RINDC.RI
CEN.WYNDC.WY
CEN.FLNDC.FL
CEN.ORNDC.OR
CEN.ALNDC.AL
Nodes
CEN 3NDC 4comb 51 Edges
input 61inferred 3
overlapsinferred 3
DCisinboththeSouthandtheNortheast
Case 2. Census Region vs. Time Zone
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PacificMountain
CentralEastern
West
South
Midwest
North-east
CEN TZ
• … but where do the articulationscome from??– automatically derived from data– expert opinion
11/01/17 Cheng
CEN.Northeast
TZ.Eastern
<
CEN.Midwest><
TZ.Mountain
><
TZ.Pacific
!
CEN.South
><
><
!
TZ.Central
><
CEN.USA
CEN.West
TZ.USA
==
!
><
!
Nodes
CEN 5TZ 5
Edges
isa_CEN 4isa_TZ 4Art. 12
CEN.Midwest
CEN.USATZ.USA
TZ.Eastern
TZ.Central
TZ.Mountain
CEN.South
CEN.Northeast
CEN.West TZ.Pacific
Nodes
CEN 4comb 1TZ 4
Edges
input 7overlapsinput 6overlapsinferred 1
inferred 1
InputOutput:PossibleWorld
Top-down regional alignment
How do we know if our ‘expert articulations’ are correct?
11/01/17 Cheng
R1 R2
R3
R4
R5
R6 R7
R8
R9
GIS solution as the Ground Truth..
11/01/17 Cheng
R1
R2
R3
R4
R5
R6
R7
R8
R9
CEN.Midwest
CEN.USATZ.USA
CEN.West
CEN.NortheastTZ.Eastern\CEN.Midwest
TZ.Eastern\CEN.South
CEN.South
CEN.South*TZ.CentralTZ.Central\CEN.Midwest
CEN.South\TZ.Eastern
CEN.South\TZ.Mountain
TZ.Central
CEN.Midwest\TZ.Eastern
TZ.Mountain\CEN.SouthTZ.Mountain
CEN.Midwest\TZ.Mountain
TZ.Mountain\CEN.Midwest
CEN.Midwest*TZ.Mountain
CEN.Midwest\TZ.Central
TZ.Mountain\CEN.West
CEN.Midwest*TZ.Eastern
CEN.West*TZ.Mountain
CEN.South*TZ.MountainCEN.South\TZ.Central
TZ.Eastern
CEN.South*TZ.Eastern
CEN.Midwest*TZ.CentralTZ.Central\CEN.South
TZ.PacificCEN.West\TZ.Mountain
Nodes
CEN 4newComb 18comb 1TZ 4
Edges
input 6inferred 37
Combined concepts solution for regional-level alignments
Does the taxonomies have to be spatial in order to use RCC-5?
• The more typical cases for taxonomy alignment are usually between non-spatial taxonomies– for which no “GIS route” or direct visual cues
about regional extensions are available– the use of RCC-5 as an alignment vocabulary is a
suitable approach to perform a wide range of multi-hierarchy reconciliations
11/01/17 Cheng
Conclusion & Discussion
• Underscores the benefits of designing different alignment workflows (Bottom-up vs. Top-Down)– Bottom-up: non-overlapping relationships at the
lowest-level articulations, not sure how to align the higher-level concepts
– Top-Down: when there is often overlapping leaf-level relations.. Expert input will frequently be needed to establish such expectations under the top-down approach
11/01/17 Cheng
https://github.com/EulerProject/[email protected]
Implications
• Logic-based taxonomy alignment approach– Disambiguate name-based taxonomy alignment over time
• 40% of the concepts in biology taxonomies undergoes name change over time (Franz et al., 2016)
– May mitigate problems in equivalent crosswalking• Membership condition problem that was often criticized in
crosswalking– Preserves the original taxonomies while providing an
alignment view• Solve data integration problems that happen in the more
coarse-grained relative crosswalking
11/01/17 Cheng
https://github.com/EulerProject/[email protected]
Acknowledgements
Support of the authors’ research through the National Science Foundation is kindly acknowledged (DEB-1155984, DBI-1342595, and DBI-1643002).
The authors thank Professor Kathryn La Barre for her comments and suggestions. We would also like to thank Dr. Laetitia Navarro and Jeff Terstriep for help with creating map overlays in QGIS.
11/01/17 Cheng
Case 1. CEN vs. NDC
• Input file
11/01/17 Cheng
taxonomyCENCensus_Regions(USANortheastMidwestSouthWest)(NortheastCTMAMENHNJNYPARIVT)(MidwestILINIAKSMIMNMONENDOHSDWI)(SouthALARDEDCFLGAKYLAMDMSNCOKSCTNTXVAWV)(WestAZCACOIDMTNVNMORUTWAWY)
taxonomyNDCNational_Diversity_Council(USAMidwestNortheastSoutheastSouthwestWest)(NortheastCTDCDEMDMAMENHNJNYPARIVT)(MidwestIAILINKSMIMNMONDNEOHSDWI)(SoutheastALARFLGAKYLAMSNCSCTNVAWV)(SouthwestAZNMOKTX)(WestCACOIDMTNVORWAWYUT)
articulationsCENNDC[CEN.ALequalsNDC.AL][CEN.ARequalsNDC.AR][CEN.AZequalsNDC.AZ][CEN.CAequalsNDC.CA][CEN.COequalsNDC.CO][CEN.CTequalsNDC.CT][CEN.DCequalsNDC.DC][CEN.DEequalsNDC.DE][CEN.FLequalsNDC.FL][CEN.GAequalsNDC.GA][CEN.IAequalsNDC.IA][CEN.IDequalsNDC.ID][CEN.ILequalsNDC.IL]…
Case 2. CEN vs. TZ
• Input file
11/01/17 Cheng
taxonomyCENCensus_Regions(USAMidwestSouthWestNortheast)taxonomyTZTime_Zone(USAPacificMountainCentralEastern)
articulationsCENTZ[CEN.Midwest disjointTZ.Pacific][CEN.Midwest overlapsTZ.Eastern][CEN.Midwest overlapsTZ.Mountain][CEN.Northeast is_included_in TZ.Eastern][CEN.South disjointTZ.Pacific][CEN.South overlapsTZ.Central][CEN.South overlapsTZ.Eastern][CEN.South overlapsTZ.Mountain][CEN.USAequalsTZ.USA][CEN.West disjointTZ.Central][CEN.West disjointTZ.Eastern][CEN.West overlapsTZ.Mountain]