euler: a logic‐based toolkit for aligning & reconciling multiple taxonomic perspectives

Euler: A Logic-‐Based Toolkit for Aligning and Reconciling Mul:ple Taxonomic

Perspec:ves

Mingmin Chen1 Shizhuo Yu1 Parisa Kianmajd1 Nico Franz2 Shawn Bowers3 Bertram Ludäscher 4

1 Dept. of Computer Science , University of California, Davis 2 School of Life Sciences, Arizona State University 3 Dept. of Computer Science, Gonzaga University

4 GSLIS & NCSA, University of Illinois at Urbana-‐Champaign

Outline •  Meet Nico, Curator of Insects

•  TAP: The Taxonomy Alignment Problem

•  Euler/X – Logic Inside! (X in FOL, RCC, ASP)

•  Related Projects

B. Ludäscher Euler: Reasoning about Taxonomies CIRSS Seminar 9/19/2014 2

Meet Prof. Nico Franz: Curator of Insects @ ASU


What Nico et al. do for a living …


Perelleschus salpinflexus sec. Franz & Cardona-‐Duque (2013) DOI:10.1080/14772000.2013.806371

1 Input ar:cula:ons: Franz & Cardona-‐Duque. 2013. Descripaon of two new species and phylogeneac reassessment of Perelleschus Wibmer & O'Brien, 1986 (Coleoptera: Curculionidae), with a complete taxonomic concept history of Perelleschus sec. Franz & Cardona-‐Duque, 2013. 2013. Systema5cs and Biodiversity 11: 209–236. Merge analyses: Franz et al. 2014. Reasoning over taxonomic change: exploring alignments for the Perelleschus use case. PLoS ONE. (in press)

Use Case: Perelleschus sec. 2001 & 2006 1


T1: Perelleschus sec. 2001 •  Phylogeneac revision •  8 ingroup species concepts •  2 outgroup concepts •  18 concepts total

T2: Perelleschus sec. 2006 •  Exemplar analysis •  2 ingroup species concepts •  1 outgroup concept •  7 concepts total

Goal: Align two phylogenies with differen:al taxon sampling

Source: Nico Franz. Explaining taxonomy's legacy to computers – how and why? The Meaning of Names: Naming Diversity in the 21st Century, Museum of

Natural History, U of Colorado, 9/30/2014.


What Nico does for a living (cont’d): The Indoors Part

•  Go fun places, find new bugs, study them … –  “Bugs-‐R-‐Us” (see taxonbytes.org)

•  Now: Compare, align and revise taxonomies, based on careful observaaon, “character” data, experase …

•  Formally: –  Input: T1 + T2 (taxonomies) + A (expert ar3cula3ons)

–  Output: revised, “merged” taxonomy (-‐ies) T3


•  Given: –  Taxonomies T1 , T2

•  incl. constraints (coverage, disjointness) –  Set of articulations (an alignment) A

•  Find: –  Combined (“merged”) taxonomy T3 (= T1 + T2 + A)

•  Is it a taxonomy? Or a DAG? –  Optional:

•  Final alignment (should be minimal)

Taxonomy Alignment Problem (TAP)

T1

T2

T3 A


Real Example: Turn this …

1.16

1.17

1.20

2.40

< OR ==

1.18

1.19

2.41

==

1.14

1.15

2.36

!

2.38

< OR ==

2.39

==

1.12

1.13

1.12L

!

2.37

==

1.11

2.42

==

2.43

==

1.27 2.50==

1.23

1.25

1.24

2.53

> OR !

2.52

> OR !

2.47

< OR ==

2.54

> OR !

1.22

2.46

==

1.21

2.45

==

2.44

< OR ==

1.26 2.49==2.48

==2.51

==

2.35

2.36L

Nodes

1 18

2 21

Edges

isa_1 17

isa_2 20

Art. 20


… into this! (Perellescus Alignment Result)

•  T3 := T1 and T2 are “merged” –  Blue dashed: overlaps è resolve via “zoom-in view”

1.16

1.14

2.40

2.44

2.47

1.11

2.382.35

1.20

1.23

2.52

2.53

2.54

1.172.41

1.222.46

1.252.48

1.122.36

1.262.49

1.132.37

1.182.42

1.192.43

1.152.39

1.212.45

1.12L2.36L

1.272.50

1.242.51

Nodes

Taxonomy 1 5Taxonomy 2 8

MERGED Taxa 13 Edges

Overlaps 10Input 24

INFERRED 5


So how does it work? •  If you have 3 concepts A, B, and C. •  Assume you know something about

– A óR1 B (e.g. R1: A is a subset of B) – B óR2 C (e.g., R2: B is disjoint from C)

•  Now what can you say about this: – A óR3 C

•  Yes ?? •  … it follows that R3: A is disjoint from C!


Ar:cula:on Language (RCC-‐5) •  How does the expert express the known (or assumed) relaaonship between taxa A and B?

•  How can A and B be related? •  Use basic set constraints (B5):

– A = B (equals EQ) (==) – A < B (proper part of PP) (<) – A > B (inverse proper part of IPP) (>) – A o B (paraally overlaps PO) (><) – A ! B (disjoint “region” DR) (!)


Taxonomies and Ar:cula:ons in Euler

There are 32 (= 25) possible disjunc:ons for represenang par:al informa:on.

A taxonomy T is a triple (N, ≼, ϕ) with names (taxa) N, a paraal order (is-‐a) ≼, and taxonomic constraints ϕ.

•  Sibling Disjointness: sibling taxa do not overlap •  (Parent) Coverage: The union of the children “covers” the

parent è no “missing” children

A B

(iv) par5al overlap

A B

(ii) proper part

B A

(iii) Inverse proper part

A B

(i) congruence

A B

(v) disjointness

An ar:cula:on is a relaaon (set-‐constraint) between taxa A and B. One, and only one, of the following base relaaons B5 must hold:


R32 lahce of 32 (=25) disjunc:ons over B5


= < > o !(TRUE)

= < > != < > o < > o != > o != < o !

= < > < > != > != < ! < > o= > o= < o > o !< o != o !

< >= >= < > !< != ! > o< o= o o !

><= !o

∅(FALSE)

= EQ(x,y) Equals< PP(x,y) Proper Part of> iPP(x,y) Inverse Proper Parto PO(x,y) Partially Overlaps! DR(x,y) Disjoint from

Level 1(BASE-5 relations)

Level 2

Level 3

Level 4

Level 5(tautology)

Level 0(contradiction)

•  … Aristotle … •  … Euler … •  … •  … Greg Whitbread …

•  [BPB93] J. H. Beach, S. Pramanik, and J. H. Beaman. Hierarchic taxonomic databases.,Advances in Computer Methods for Systematic Biology: Artificial Intelligence, Databases, Computer Vision, 1993

•  [Ber95] Walter G. Berendsohn. The concept of “potential taxa” in databases. Taxon, 44:207–212, 1995.

•  [Ber03] Walter G. Berendsohn. MoReTax – Handling Factual Information Linked to Taxonomic Concepts in Biology. No. 39 in Schriftenreihe für Vegetationskunde. Bundesamt für Naturschutz, 2003.

•  [GG03] M. Geoffroy and A. Güntsch. Assembling and navigating the potential taxon graph. In [Ber03], pages 71–82, 2003.

•  [TL07] Thau, D., & Ludäscher, B. (2007). Reasoning about taxonomies in first-order logic. Ecological Informatics, 2(3), 195-209.

•  [FP09] Franz, N. M., & Peet, R. K. (2009). Perspectives: towards a language for mapping relationships among taxonomic concepts. Systematics and Biodiversity, 7(1), 5-20.

•  …

15

Some History

B. Ludäscher Euler: Reasoning about Taxonomies CIRSS Seminar 9/19/2014

What’s in a name? Euler Diagrams

•  Project named after Euler Diagrams: IF A is-a B AND C and B are disjoint ------------------------------------ THEN: A and C are disjoint!

16 B. Ludäscher Euler: Reasoning about Taxonomies CIRSS Seminar 9/19/2014

Euler Diagrams asTrees (or Graphs) A containment hierarchy (taxonomy)

An equivalent graph (w/ transi5ve edges)

same informa:on


Represent Phylogenies as Trees …

T1: Perelleschus sec. 2001 •  Phylogeneac revision •  8 ingroup species concepts •  2 outgroup concepts •  18 concepts total

1.16

1.17 1.20

1.18 1.19

1.14

1.15

1.12

1.13 1.12L

1.11

1.27

1.23

1.25 1.24

1.22 1.21

1.26

2.41

2.42 2.43

2.35

2.36 2.38

2.37 2.36L 2.39 2.40

2.53

2.52

2.54

2.51

2.50

2.44

2.45 2.46 2.47

2.48

2.49


… for all taxonomies of interest …

1.16

1.17 1.20

1.18 1.19

1.14

1.15

1.12

1.13 1.12L

1.11

1.27

1.23

1.25 1.24

1.22 1.21

1.26

2.41

2.42 2.43

2.35

2.36 2.38

2.37 2.36L 2.39 2.40

2.53

2.52

2.54

2.51

2.50

2.44

2.45 2.46 2.47

2.48

2.49


… ready, rotate by 90o, set …

1.16

1.17 1.20

1.18 1.19

1.14

1.15

1.12

1.13 1.12L

1.11

1.27

1.23

1.25 1.24

1.22 1.21

1.26

2.41

2.40

2.35

2.37

2.36

2.39

2.38

2.53

2.52

2.47

2.51

2.50

2.48

2.422.43

2.44

2.452.46

2.49 2.54

2.36L


Go! An expert input alignment! Just add some Euler Reasoning …

1.16

1.17

1.20

2.40

< OR ==

1.18

1.19

2.41

==

1.14

1.15

2.36

!

2.38

< OR ==

2.39

==

1.12

1.13

1.12L

!

2.37

==

1.11

2.42

==

2.43

==

1.27 2.50==

1.23

1.25

1.24

2.53

> OR !

2.52

> OR !

2.47

< OR ==

2.54

> OR !

1.22

2.46

==

1.21

2.45

==

2.44

< OR ==

1.26 2.49==2.48

==2.51

==

2.35

2.36L

Nodes

1 18

2 21

Edges

isa_1 17

isa_2 20

Art. 20


Euler/X toolkit in a single screenshot (desktop version, IX-‐2014)

… et voilà! The merged T3 (=T1 & T2 & A)


The Euler reasoner(s) infer: -‐ Grey: “perfect match” (congruences) -‐ Green, Yellow: “keepers” from T1, T2 -‐ Red edges: deduced subset/“sub-‐class”relaaons -‐ Blue edges: deduced overlaps

1.16

1.14

2.40

2.442.47

1.11

2.38

2.35

1.20

1.23

2.52

2.53

2.54

1.172.41

1.222.46

1.252.48

1.122.36

1.262.49

1.132.37

1.182.42

1.192.43

1.152.39

1.212.45

1.12L2.36L

1.272.50

1.242.51

1.16

1.14

2.402.44

2.47

1.11

2.38

1.12

2.35

2.36

2.36L

1.12L

1.20

1.23

2.52

2.53

2.54

1.172.41

1.252.48

1.262.49

1.132.37

1.182.42

1.192.43

1.152.39

1.222.46

1.212.45

1.272.50

1.242.51


But wait: PW1 …

1.16

1.14

2.402.44

2.47

1.11

2.38

1.122.35

1.12L

2.36

1.20

1.23

2.52

2.53

2.54

2.36L

1.172.41

1.252.48

1.262.49

1.132.37

1.182.42

1.192.43

1.152.39

1.222.46

1.212.45

1.272.50

1.242.51


… PW2

1.16

1.14

2.40

2.442.47

1.11

2.38

1.122.36

2.36L

2.35

1.12L

1.20

1.23

2.52

2.53

2.54

1.172.41

1.252.48

1.262.49

1.132.37

1.182.42

1.192.43

1.152.39

1.222.46

1.212.45

1.272.50

1.242.51


… PW3

1.16

1.14

2.40

2.442.47

1.11

2.38

2.35

1.20

1.23

2.52

2.53

2.54

1.172.41

1.222.46

1.252.48

1.122.36

1.262.49

1.132.37

1.182.42

1.192.43

1.152.39

1.212.45

1.12L2.36L

1.272.50

1.242.51


… PW4

1.16

1.14

2.40

2.44

2.47

1.11

2.38

1.12

2.35

2.36

1.12L

1.20

1.23

2.52 2.53

2.54

2.36L

1.172.41

1.252.48

1.262.49

1.132.37

1.182.42

1.192.43

1.152.39

1.222.46

1.212.45

1.272.50

1.242.51


… PW5

1.16

1.14

2.40

2.442.47

1.11

2.38

1.122.36

2.36L

2.35

1.12L

1.20

1.23

2.52

2.53

2.54

1.172.41

1.252.48

1.262.49

1.132.37

1.182.42

1.192.43

1.152.39

1.222.46

1.212.45

1.272.50

1.242.51

Hmmm… depending on input alignment: PW1


1.16

1.14

2.40

2.442.47

1.11

2.38

2.35

1.20

1.23

2.52

2.53

2.54

1.172.41

1.222.46

1.252.48

1.122.36

1.262.49

1.132.37

1.182.42

1.192.43

1.152.39

1.212.45

1.12L2.36L

1.272.50

1.242.51

… and PW2 are the only solu:ons!


What happened?

TAP: Possible Outcomes

1.a 1.bisa

1.cisa

2.d

=

2.e<

<

2.f<isa

isa

Input Alignment



1.a 1.bisa

1.cisa

2.d

=

2.e<

<

2.f<isa

isa

Input Alignment

{A1, A2, A3, A4}

{A1, A2, A3} {A1, A2, A4} {A1, A3, A4} {A2, A3, A4}

{A1, A2} {A1, A3} {A2, A3} {A1, A4} {A2, A4} {A3, A4}

{A1} {A2} {A3} {A4}

{ }

Inconsistent! è Diagnosis (Reiter) = Black-‐Box Provenance



1.a 1.bisa

1.cisa

2.d

=

2.e<

<

2.f<isa

isa

Input Alignment

{A1, A2, A3, A4}

{A1, A2, A3} {A1, A2, A4} {A1, A3, A4} {A2, A3, A4}

{A1, A2} {A1, A3} {A2, A3} {A1, A4} {A2, A4} {A3, A4}

{A1} {A2} {A3} {A4}

{ }


1.b2.e

1.c

1.a2.d

2.f

Ambiguous! è Mul5ple Possible Worlds



1.a 1.bisa

1.cisa

2.d

=

2.e<

<

2.f<isa

isa

Input Alignment

{A1, A2, A3, A4}

{A1, A2, A3} {A1, A2, A4} {A1, A3, A4} {A2, A3, A4}

{A1, A2} {A1, A3} {A2, A3} {A1, A4} {A2, A4} {A3, A4}

{A1} {A2} {A3} {A4}

{ }


1.b2.e

1.c

1.a2.d

2.f


1.c2.f

1.b

1.a2.d

2.e



1.a 1.bisa

1.cisa

2.d

=

2.e<

<

2.f<isa

isa

Input Alignment

{A1, A2, A3, A4}

{A1, A2, A3} {A1, A2, A4} {A1, A3, A4} {A2, A3, A4}

{A1, A2} {A1, A3} {A2, A3} {A1, A4} {A2, A4} {A3, A4}

{A1} {A2} {A3} {A4}

{ }


1.b2.e

1.c

1.a2.d

2.f


1.c2.f

1.b

1.a2.d

2.e

1.b1.a

2.e

2.d1.c

2.fB. Ludäscher Euler: Reasoning about Taxonomies CIRSS Seminar 9/19/2014 35

•  FO reasoning about taxonomies (MFOL)

•  Earlier: CleanTax –  Prover9/Mace4

•  Now: Euler –  ASP Reasoners (DLV,

Clingo) –  Specialized reasoners

(PyRCC) –  … –  X = ASP, RCC, …

Euler/X Toolkit and Workflow


Reducing Ambiguity

Possible Worlds (PWs) View

Aggregate View (AV) Cluster View

(CV)

Explore!


Common Outcome: Inconsistency!

1.a 1.bisa

1.cisa

2.d

=

2.e<

<

2.f<isa

isa

Input Alignment

{A1, A2, A3, A4}

{A1, A2, A3} {A1, A2, A4} {A1, A3, A4} {A2, A3, A4}

{A1, A2} {A1, A3} {A2, A3} {A1, A4} {A2, A4} {A3, A4}

{A1} {A2} {A3} {A4}

{ }


•  Need to debug the input araculaaons è (black-‐box) diagnosis!

•  Focus: –  How do we efficiently compute the diagnosac lauce?

•  Also: –  How to visualize..


A Hybrid Diagnosis Approach Combining Black-‐Box and White-‐Box Reasoning

Mingmin Chen1 Shizhuo Yu1 Nico Franz2 Shawn Bowers3 Bertram Ludäscher 4

1 Department of Computer Science , University of California, Davis 2 School of Life Sciences, Arizona State University

3 Department of Computer Science, Gonzaga University 4 GSLIS & NCSA, University of Illinois at Urbana-‐Champaign

Example Instance (from syntheac benchmark suite)

•  Here: N = 10 taxa in T1, T2 •  Euler/X finds:

inconsistent! •  è diagnos:c lahce of 210

= 1024 nodes è  Find minimal inconsistent

subset (MIS) è maximal consistent subset

(MCS) .. è  show to user!


Visualizing Diagnoses

N = 10 araculaaons è 210 = 1024 node diagnosac lauce B. Ludäscher Euler: Reasoning about Taxonomies CIRSS Seminar 9/19/2014 41

Bener Idea: Just show MIS, MCS

N = 4 araculaaons è 24 = 16 node diagnosac lauce, but 3 MCS and 2 MIS are enough!


Visualizing Diagnoses

.. but 4 MCS and 1 MIC tell it all!

1024 node lauce


Visualizing Diagnoses Example from RuleML’14 paper: N=12 è 4096 nodes .. but 7 MCS and 5 MIC tell it all!


Black-Box Inconsistency Analysis (Diagnostic Lattice)

•  Then: –  Repair: find & revise minimal inconsistent subsets (Min-Incons) –  Expand: find maximal consistent subsets (Max-Cons) & revise outs

What happens if you can’t have all (here: 4) articulations together?


•  Black-‐box Analysis (Hiung Set algo.) yields a Diagnosis (lauce) –  for n=4 araculaaons, there are 168 possible diagnoses –  depending on expected “red/green areas” è explore space differently

•  |araculaaons| = n è |possible diagnoses| = |monotonic Boolean funcaons| = Dedekind Number (n): 2, 3, 6, 20, 168, 7581, 7828354, ...

Inconsistency Analysis (Diagnostic Lattice)

•  The Min-Incons (MIS) and Max-Cons (MCS) sets determine all others

è  Repair MIS and/or Expand MCS


Improving Diagnosis •  Reiter’s “black-‐box” (model-‐based) diagnosis helps debug the araculaaons

•  Limited scalability (inherent complexity) •  But every bit helps:

– Hiung Set Algorithm (“logarithmic extracaon”)

•  Our idea: – Exploit “white-‐box” reasoning informaaon è RULES to the rescue


Key Idea: exploit white-‐box info •  We use Answer Set Programming (ASP) to solve Taxonomy Alignment Problem (TAP)

•  Inconsistency = “False” is derived in the head: False :-‐ <denial of integrity constraint>

•  Apply provenance trick from databases J – What araculaaons contribute to a derivaaon of “False” ? –  Eliminate those that don’t! è an example of reusing inferences across separate black-‐box tests!


The Provenance “Trick”


Hybrid Provenance

A3: c < f Black-‐box Provenance

1.a 1.bisa

1.cisa

2.d

=

2.e<

<

2.f<isa

isa

Input Alignment


Hybrid Provenance

A3: c < f Black-‐box Provenance

r7: d = e ∪ f

a = e ∪ f

A1: a = d

r3: a = b ∪ c

f < c

r4: b ∩ c = ∅ r8: e ∩ f = ∅ A2: b < e

A1+A2 + … => f < c

White-‐box Provenance

1.a 1.bisa

1.cisa

2.d

=

2.e<

<

2.f<isa

isa

Input Alignment


The Hybrid Approach


Hybrid Approach

What ar5cula5ons contribute to some inconsistency?

Good old black-‐box (HST)


Benchmark Results

•  White-‐box < Hybrid < Black-‐box (runames) •  Note: white-‐box does not give you a diagnosis •  Potassco < DLV


Benchmark DLV

•  White-‐box < Hybrid < Black-‐box (runames) •  Potassco < DLV


Benchmark Clingo

•  White-‐box < Hybrid < Black-‐box (runames) •  Potassco < DLV


Summary: Hybrid Diagnosis •  ASP rules can be used to efficiently solve real-‐world taxonomy reasoning problems

•  Reiter’s diagnosis useful to debug inconsistent alignments

•  Adding a “white-‐box” provenance approach speeds up state-‐of-‐the-‐art HST algorithm by elimina:ng independent ar:cula:ons

•  Future work: – Further improvements, including parallelism:

•  Trade-‐off with sharing inferences across parallel instances


Related Projects


The Data Life Cycle


Data Quality & Curation Workflows •  Collections & occurrence data is

all over the map –  … literally (off the map!)

•  Issues: –  Lat/Long transposition,

coordinate & projection issues –  Data entry/creation, “fuzzy”

data, naming issues, bit rot, data conversions and transformations, schema mappings, … (you name it)

•  Filtered-Push Collaboration


Filtered-Push: Kurator (Data Curation Workflows)

Tianhong Song

Lei Dou (former member)

Sven Köhler


From Tool Users to Tool Makers

Screen capture… back to the original definition


Theory meets Prac:ce


Under the hood: Logic (ASP)


Summary & Invita:on •  Building open source tools for

–  Euler: Reasoning about taxonomies (& data integraaon) –  Kurator: Data Curaaon workflows

•  … and other scienafic workflows

•  Topic not covered: –  (Game) Theory of Provenance (DAIS talk @CS, 10/7/2014)

•  Looking for: –  new collaborators, students, ..

•  Let’s meet! –  [email protected]


euler: a logic‐based toolkit for aligning & reconciling multiple taxonomic perspectives

Science

y proper

t2 taxonomies t1

y disjoint fromlevel

final alignment

y equals ppx

euler diagrams project

combined merged taxonomy

y inverse proper parto