Your logical axioms might be inconsistent? Use this approach to speed up your model-based diagnosis! Presented at RuleML'14 in August in Prague (co-located with ECAI 2014).

1. A
Hybrid
Diagnosis
Approach
Combining
Black-­‐Box
and
White-­‐Box
Reasoning
Mingmin
Chen1
Shizhuo
Yu1
Nico
Franz2
Shawn
Bowers3
Bertram
Ludäscher1
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

2. Outline
• The
Taxonomy
Alignment
Problem
T1
+
T2
+
A
=>
T3
(ambiguous
..
unique
..
inconsistent)
• Model-­‐based
Diagnosis
[Reiter’87]
– Black-­‐box
• Hybrid
Approach
– Black-­‐box
&
White-­‐box
combined
• Benchmark
Results
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
2

3. Meet
Prof.
Nico
Franz:
Curator
of
Insects
@
ASU
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
3

4. What
Nico
et
al.
do
for
a
living
…
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
4

5.
What
Nico
does
for
a
living
(cont’d):
The
Indoors
Part
• First:
go
fun
places,
find
new
bugs,
study
them
…
– “Bugs-­‐R-­‐Us”
(see
taxonbytes.org)
• Now:
Compare,
align
and
revise
taxonomies,
based
on
careful
observafon,
“character”
data,
experfse
…
• Formally:
– Input:
T1
+
T2
(taxonomies)
+
A
(expert
ar.cula.ons)
– Output:
revised,
“merged”
taxonomy
(-­‐ies)
T3
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
5

6. • Given:
– Taxonomies T1 , T2
• incl. constraints (coverage, disjointness)
– Set of articulations (alignment) A
• Find:
– Combined (“merged”) taxonomy T3 (= T1 + T2 + A)
• Is it a taxonomy? Or a DAG?
– Optional:
• Final alignment (should be minimal)
6
Taxonomy Alignment Problem (TAP)
T1
T2
A
T3

7.
TAP:
Possible
Outcomes
1.a
1.b
isa
1.c
isa
2.d
=
2.e<
<
2.f<
isa
isa
Input
Alignment
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
7

8.
TAP:
Possible
Outcomes
1.a
1.b
isa
1.c
isa
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
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
8

9. TAP:
Possible
Outcomes
1.a
1.b
isa
1.c
isa
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.b2.e
1.c
1.a
2.d
2.f
Ambiguous!
è
Mul5ple
Possible
Worlds
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
9

10. TAP:
Possible
Outcomes
1.a
1.b
isa
1.c
isa
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.b2.e
1.c
1.a
2.d
2.f
Ambiguous!
è
Mul5ple
Possible
Worlds
1.c2.f
1.b
1.a
2.d
2.e
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
10

11. TAP:
Possible
Outcomes
1.a
1.b
isa
1.c
isa
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.b2.e
1.c
1.a
2.d
2.f
Ambiguous!
è
Mul5ple
Possible
Worlds
1.c2.f
1.b
1.a
2.d
2.e
1.b
1.a
2.e
2.d
1.c
2.f
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
11

12. • 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
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
12

13. Real-­‐world
examples:
Turn
this
…
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
13

14. … into this!
(Perellescus Alignment Result)
• T3 := T1 and T2 are “merged”
– Blue dashed: overlaps è resolve via “zoom-in view”
14
1.16
1.14
2.40
2.44
2.47
1.11
2.38
2.35
1.20
1.23
2.52
2.53
2.54
1.17
2.41
1.22
2.46
1.25
2.48
1.12
2.36
1.26
2.49
1.13
2.37
1.18
2.42
1.19
2.43
1.15
2.39
1.21
2.45
1.12L
2.36L
1.27
2.50
1.24
2.51
Nodes
Taxonomy 1 5
Taxonomy 2 8
MERGED Taxa 13
Edges
Overlaps 10
Input 24
INFERRED 5

15.
Possible
Outcome:
Inconsistency!
1.a
1.b
isa
1.c
isa
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
• Need
to
debug
the
input
arfculafons
è
(black-­‐box)
diagnosis!
• Focus:
– How
do
we
efficiently
compute
the
diagnosfc
lance?
• Also:
– How
to
visualize..
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
15

16. Example
Instance
(from
synthefc
benchmark
suite)
• Here:
N
=
10
taxa
in
T1,
T2
• Euler/X
finds:
inconsistent!
• è
diagnosc
la]ce
of
210
=
1024
nodes
è Find
minimal
inconsistent
subset
(MIS)
è maximal
consistent
subset
(MCS)
..
è show
to
user!
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
16

17. Visualizing
Diagnoses:
Scalability
Issues
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
17
N
=
10
arfculafons
è
210
=
1024
node
diagnosfc
lance
(…
ouch!)
…
but
only
one
MIS
…

18. Beaer
Idea:
Just
show
MIS,
MCS
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
18
N
=
4
arfculafons
è
24
=
16
node
diagnosfc
lance,
but
3
MCS
and
2
MIS
are
enough!

19. ..
but
4
MCS
and
1
MIC
tell
it
all!
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
19
1024
node
lance
Visualizing
Diagnoses:
Focusing
on
MIS
(and
MCS)

20. Visualizing
Diagnoses
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
20
Example
from
paper:
N=12
è
4096
nodes
..
but
7
MCS
and
5
MIC
tell
it
all!

21. 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?
21

22. • Black-­‐box
Analysis
(Hinng
Set
algo.)
yields
a
Diagnosis
(lance)
– for
n=4
arfculafons,
there
are
168
possible
diagnoses
– depending
on
expected
“red/green
areas”
è
explore
space
differently
• |arfculafons|
=
n
è
|possible
diagnoses|
=
|monotonic
Boolean
funcfons|
=
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
22

23. Improving
Diagnosis
• Reiter’s
“black-­‐box”
(model-­‐based)
diagnosis
helps
debug
the
arfculafons
• Limited
scalability
(inherent
complexity)
• But
every
bit
helps:
– Hinng
Set
Algorithm
(“logarithmic
extracfon”)
• Our
idea:
– Exploit
“white-­‐box”
reasoning
informafon
è
RULES
to
the
rescue
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
23

24. 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
arfculafons
contribute
to
a
derivafon
of
“False”
?
– Eliminate
those
that
don’t!
è
an
example
of
reusing
inferences
across
separate
black-­‐box
tests!
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
24

25. The
Provenance
“Trick”
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
25

26. Hybrid
Provenance
A3:
c
<
f
Black-­‐box
Provenance
1.a
1.b
isa
1.c
isa
2.d
=
2.e<
<
2.f<
isa
isa
Input
Alignment
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
26

27. 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.b
isa
1.c
isa
2.d
=
2.e<
<
2.f<
isa
isa
Input
Alignment
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
27

28. The
Hybrid
Approach
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
28

29. Hybrid
Approach
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
29
What
ar5cula5ons
contribute
to
some
inconsistency?
Good
old
black-­‐box
(HST)

30. Benchmark
Results
• White-­‐box
<
Hybrid
<
Black-­‐box
(runfmes)
• Note:
white-­‐box
does
not
give
you
a
diagnosis
• Potassco
<
DLV
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
30

31. Benchmark
DLV
• White-­‐box
<
Hybrid
<
Black-­‐box
(runfmes)
• Potassco
<
DLV
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
31

32. Benchmark
Clingo
• White-­‐box
<
Hybrid
<
Black-­‐box
(runfmes)
• Potassco
<
DLV
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
32

33. Conclusions
• 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
eliminang
independent
arculaons
• Future
work:
– Further
improvements,
including
parallelism:
• Trade-­‐off
with
sharing
inferences
across
parallel
instances
Hybrid
Diagnosis
in
Euler
@
RuleML2014,
Prague
33