Towards a Logic Formalization of Taxonomic Concepts

1
Towards a Logic Formalization of Taxonomic
Concepts

• Dave Thau, Bertram Ludäscher, Shawn Bowers
• UC Davis
• thau_at_learningsite.com

2
Names are Confusing
Adapted from R. Peet
Ranunculus plumosa
R.plumosa var intermedia
R.plumosa var plumosa
Ranunculus pinetcola
Ranunculus plumosa
Ranunculus plumosa
Ranunculus homunculus
3
Impact on Data Analysis

• Cant find data
• If A º B, a search on A should retrieve B
• Same if A ? B
• Cant aggregate data
• If A ? B, you should be able to combine data from
  A into B

4
Where In Greece Can I Find Ranunculus aquatilis?
?
R. aquatilis
R. trichophyllus
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Mapping Taxonomies
FNA-03, 1997
Benson, 1948
?
Ranunculus aquatilis
Ranunculus aquatilis
º
R.a. var aquatilis
R.a. var diffusus
R.a. var hispidulus
R.a. var capillaceus
R.a. var calvescens
º
?
º
?
This results in 512 (more than 240 million)
possible sets of relationships.
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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

7
Logic, why?

• Precise modeling language
• Solid mathematical basis
• Good tools for reasoning are available
• Explicit, portable representation (not buried
  in code)

8
Basic Taxonomy
A

• Rooted tree
• Only Isa relations

isa
isa
B
C
B
A
C
A
In the basic taxonomy ??T???isa?T?
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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) ?
• ?n1 m ? E, n2
  m ? E, T(N,E))
• Closed World
• A node with children is defined as the union of
  those children
• This ones formula is a bit long trust me

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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
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Inferring Unstated Correspondences

Benson, 1948
Kartesz, 2004
Ranunculus arizonicus
Ranunculus arizonicus
Given º
Given ?
R.a. var chihuahua
R.a. var typicus
We can demonstrate ?
Peet, 2005 B.1948R.a.typicus is included in
K.2004R. arizonicus B.1948R. arizonicus is
congruent to K.2004R. arizonicus
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Proving New Mappings
Benson, 1948
Kartesz, 2004
A Ranunculus arizonicus
D Ranunculus arizonicus
º
?
B R.a. var chihuahua
C R.a. var typicus
? ?
Show B ? D and ?(D ? B)
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Formal Proof of Mapping
Part 1
Part 2
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Inconsistent Mapping
Benson, 1948
Kartesz, 2004
Ranunculus hydrocharoides
Ranunculus hydrocharoides
º
R.h. var natans
R.h. var stolonifer
R.h. var typicus
R.h. var stolonifer
R.h. var typicus
º
º
Peet, 2005 B.1948R.h.stolonifer is congruent
to K.2004R.h.stolonifer B.1948R.h.typicus is
congruent to K.2004R.h.typicus B.1948R.
hydrocharoides is congruent to K.2004R.
hydrocharoides
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Proving Inconsistency
Benson, 1948
Kartesz, 2004
Ranunculus hydrocharoides
Ranunculus hydrocharoides
º
R.h. var natans
R.h. var stolonifer
R.h. var typicus
R.h. var stolonifer
R.h. var typicus
º
º
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Formal Proof of Inconsistency
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Showing Inconsistency Using Popular Tools
Benson, 1948
Kartesz, 2004
Ranunculus
Ranunculus
Ranunculus petiolaris
Ranunculus petiolaris
Ranunculus macranthus


?
??
B.48R. petiolaris ? K.04R. petiolaris ? B.48R.
macranthus contradicts
B.48R. macranthus and B.48R. petiolaris are
disjoint.
Peet, 2005 B.1948R. macranthus contains
K.2004 R. petiolaris B.1948R. petiolaris is
contained by K. petiolaris
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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.

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Inconsistent Mapping
Benson, 1948
Kartesz, 2004
Ranunculus hydrocharoides
Ranunculus hydrocharoides
º
R.h. var natans
R.h. var stolonifer
R.h. var typicus
R.h. var stolonifer
R.h. var typicus
º
º
Peet, 2005 B.1948R.h.stolonifer is congruent
to K.2004R.h.stolonifer B.1948R.h.typicus is
congruent to K.2004R.h.typicus B.1948R.
hydrocharoides is congruent to K.2004R.
hydrocharoides
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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

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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

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Thanks! Questions?

• We would like to acknowledge
• Bob Peet for the Ranunculus data set
• NSF, under SEEK awards 0225676, 0225665, 0225635,
  and 0533368