1. Towards a Logic Formalization of Taxonomic Concepts
Dave Thau, Bertram Ludäscher, Shawn Bowers
UC Davis

2. 5th International Conference on Ecological Informatics
Names are Confusing
Adapted from R. Peet
Ranunculus
plumosa
Gray
1834
R.plumosa
var
intermedia
R.plumosa
var
plumosa
Chapman
1860
Kral
1998
Ranunculus
pinetcola
Ranunculus
plumosa
Ranunculus
plumosa
Ranunculus
homunculus
Thau
2006
5th International Conference on Ecological Informatics

3. Impact on Data Analysis
Can’t find data
If A º B, a search on A should retrieve B
Same if A  B
Can’t aggregate data
If A  B, you should be able to combine data from A into B
5th International Conference on Ecological Informatics

4. 5th International Conference on Ecological Informatics
Where In Greece Can I Find Ranunculus aquatilis?
R. aquatilis 
R. trichophyllus
5th International Conference on Ecological Informatics

5. 5th International Conference on Ecological Informatics
Mapping Taxonomies
Benson, 1948
FNA-03, 1997
Ranunculus
aquatilis 
Ranunculus
aquatilis
R.a. var
calvescens
R.a. var
capillaceus
R.a. var
aquatilis
R.a. var
diffusus
R.a. var
hispidulus  B A
A  B B A
A  B
B  A B A
A overlap B B A
A disjoint B 
This results in 512 (more than 240 million) possible sets of relationships.
5th International Conference on Ecological Informatics

6. 5th International Conference on Ecological Informatics
Overview
The problems – Names change, experts disagree, data become incomparable
The partial solution – Taxonomic Concepts
Another part of the solution – Logic
Representing taxonomy in logic
Using the representation to detect inconsistencies and discover new relations
Applications
5th International Conference on Ecological Informatics

7. 5th International Conference on Ecological Informatics
Logic, why?
Precise modeling language
Solid mathematical basis
Good tools for reasoning are available
Explicit, “portable” representation (not buried in code)
5th International Conference on Ecological Informatics

8. 5th International Conference on Ecological Informatics
Basic Taxonomy A
Rooted tree
Only “Isa” relations
isa
isa B C
T = (N, E)
N = {A, B, C}
E = {B A, C A} 
isa B 
isa A 
isa C A
isaTx:m(x)  n(x)m n  E, T=(N,E)) } 
isa
In the basic taxonomy TisaT
5th International Conference on Ecological Informatics

9. Some Additional Constraints
No empty nodes
All nodes have at least one element
Tx: n(x)n  N, T=(N,E)) }
Disjointness
The children of a node are disjoint
!Tx: n1(x)  n2(x) 
n m  E, n m  E, T=(N,E)) }
Closed World
A node with children is defined as the union of those children
This one’s formula is a bit long – trust me… A B C
isa 
isa 
isa
5th International Conference on Ecological Informatics

10. 5th International Conference on Ecological Informatics
Mapping Formulae
Mappings between nodes in two different taxonomies have their owns
In the slides and proofs to come I will use these symbols:
A  B: A is included in B
A  B: A includes B
A  B: A and B are equivalent
5th International Conference on Ecological Informatics

11. Inferring Unstated Correspondences
Benson, 1948
Kartesz, 2004
Ranunculus
arizonicus
Given: º
Ranunculus
arizonicus
Given: 
R.a. var
chihuahua
R.a. var
typicus
We can demonstrate: 
Peet, 2005:
B.1948:R.a.typicus is included in K.2004:R. arizonicus
B.1948:R. arizonicus is congruent to K.2004:R. arizonicus
5th International Conference on Ecological Informatics

12. 5th International Conference on Ecological Informatics
Proving New Mappings
Benson, 1948
Kartesz, 2004 A
Ranunculus
arizonicus D
Ranunculus
arizonicus  B
R.a. var
chihuahua C
R.a. var
typicus
 ?
Show B  D and (D  B)
5th International Conference on Ecological Informatics

13. Formal Proof of Mapping
Part 1
Part 2
5th International Conference on Ecological Informatics

14. 5th International Conference on Ecological Informatics
Inconsistent Mapping
Benson, 1948
Kartesz, 2004
Ranunculus
hydrocharoides
Ranunculus
hydrocharoides
R.h. var
natans
R.h. var
stolonifer
R.h. var
typicus
R.h. var
stolonifer
R.h. var
typicus
Peet, 2005:
B.1948:R.h.stolonifer is congruent to K.2004:R.h.stolonifer
B.1948:R.h.typicus is congruent to K.2004:R.h.typicus
B.1948:R. hydrocharoides is congruent to K.2004:R. hydrocharoides
5th International Conference on Ecological Informatics

15. Proving Inconsistency
Benson, 1948
Kartesz, 2004
Ranunculus
hydrocharoides
Ranunculus
hydrocharoides
R.h. var
natans
R.h. var
stolonifer
R.h. var
typicus
R.h. var
stolonifer
R.h. var
typicus
good – you could animate and ask “does someone see the problem”
then (either way), you show the reasoning.
do NOT show the formulas first, but give an “abstract proof”
have a formal proof as back-up (but essentially you’ll have to skip over)
GOAL:
1. convince audience that the reasoning makes sense
2. convince audience that there is an algorithm that could have done the reasoning for us..
5th International Conference on Ecological Informatics

16. Formal Proof of Inconsistency
5th International Conference on Ecological Informatics

17. Showing Inconsistency Using Popular Tools
Benson, 1948
Kartesz, 2004
Ranunculus
Ranunculus
Ranunculus
macranthus
Ranunculus
petiolaris
Ranunculus
petiolaris … …  
B.48:R. petiolaris  K.04:R. petiolaris  B.48:R. macranthus contradicts
B.48:R. macranthus and B.48:R. petiolaris are disjoint.
Peet, 2005:
B.1948:R. macranthus contains K.2004: R. petiolaris
B.1948:R. petiolaris is contained by K. petiolaris
5th International Conference on Ecological Informatics

18. Resolving Inconsistencies
Trying to simultaneously satisfy no emptiness, disjointness and the closed world
Relaxing any of these makes the mapping consistent – giving us clues to hidden truths
It turns out that Kartesz and Benson focus on different localities.
5th International Conference on Ecological Informatics

19. 5th International Conference on Ecological Informatics
Inconsistent Mapping
Benson, 1948
Kartesz, 2004
Ranunculus
hydrocharoides
Ranunculus
hydrocharoides
R.h. var
natans
R.h. var
stolonifer
R.h. var
typicus
R.h. var
stolonifer
R.h. var
typicus
Peet, 2005:
B.1948:R.h.stolonifer is congruent to K.2004:R.h.stolonifer
B.1948:R.h.typicus is congruent to K.2004:R.h.typicus
B.1948:R. hydrocharoides is congruent to K.2004:R. hydrocharoides
5th International Conference on Ecological Informatics

20. 5th International Conference on Ecological Informatics
Summary
Taxonomic Concepts are important
Logic is a useful tool when reasoning about mappings between taxonomies
We have the beginnings of a representation for taxonomies
That representation can find unstated mappings
And detect inconsistent mappings
5th International Conference on Ecological Informatics

21. 5th International Conference on Ecological Informatics
Future Work
Beefing up the representation
Formalizing more constraints, such as rank
Working in other factors, such as locality
Adding ‘intelligence’ to tools which build mappings
Using the representation in a workflow system to aid data integration
5th International Conference on Ecological Informatics

22. 5th International Conference on Ecological Informatics
Thanks! Questions?
We would like to acknowledge:
Bob Peet for the Ranunculus data set
NSF, under SEEK awards , , , and
5th International Conference on Ecological Informatics