Transcript Interactive Reasoning in Large and Uncertain RDF Knowledge Bases

Interactive Reasoning in
Large and Uncertain
RDF Knowledge Bases
Martin Theobald
Joint work with:
Maximilian Dylla, Timm Meiser, Ndapa Nakashole,
Christina Tefliuodi, Yafang Wang, Mohamed Yahya,
Mauro Sozio, and Fabian Suchanek
Max Planck Institute
Informatics
French Marriage Problem
marriedTo:
person  person
x,y,z:
marriedTo(x,y) 
marriedTo(x,z)
 y=z
marriedTo_French:
person  person
...
2
French Marriage Problem
Facts in KB:
marriedTo
(Hillary, Bill)
marriedTo
(Carla, Nicolas)
marriedTo
(Angelina, Brad)
New facts or fact candidates:
marriedTo (Cecilia, Nicolas)
marriedTo (Carla, Benjamin)
marriedTo (Carla, Mick)
marriedTo (Michelle, Barack)
marriedTo (Yoko, John)
marriedTo (Kate, Leonardo)
marriedTo (Carla, Sofie)
marriedTo (Larry, Google)
1) for recall: pattern-based harvesting
x,y,z:
marriedTo(x,y)
 marriedTo(x,z)
 y=z
2) for precision:
consistency
reasoning
3
Agenda
– URDF: Reasoning in Uncertain Knowledge Bases
•
•
•
•
Resolving uncertainty at query-time
Lineage of answers
Propositional vs. probabilistic reasoning
Temporal reasoning extensions
– UViz: The URDF Visualization Frontend
• Demo!
4
URDF: Reasoning in Uncertain KB’s
[Theobald,Sozio,Suchanek,Nakashole: MPII Tech-Report‘10]
• Knowledge harvesting from the Web may yield
knowledge bases which are
– Incomplete
bornIn(Albert_Einstein,?x)  {}
– Incorrect
bornIn(Albert_Einstein,?x)  {Stuttgart}
– Inconsistent
bornIn(Albert_Einstein,?x)  {Ulm, Stuttgart}
0.7
0.2
• Combine grounding of first-order logic rules with
additional step of consistency reasoning
– Propositional – Constrained Weighted MaxSat
– Probabilistic – Lineage & Possible Worlds Semantics
 At query time!
5
Soft Rules vs. Hard Constraints
(Soft) Inference Rules vs. (Hard) Consistency Constraints
• People may live in more than one place
livesIn(x,y)  marriedTo(x,z)  livesIn(z,y)[0.6]
livesIn(x,y)  hasChild(x,z)  livesIn(z,y) [0.2]
• People are not born in different places/on different dates
bornIn(x,y)  bornIn(x,z)  y=z
• People are not married to more than one person (at the
same time, in most countries?)
marriedTo(x,y,t1)  marriedTo(x,z,t2)  y≠z
 disjoint(t1,t2)
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Soft Rules vs. Hard Constraints (ct’d)
Enforce FD‘s (e.g., mutual exclusion) as hard constraints:
livesIn(x,y)  type(y,City)  locatedIn(y,z)  type(z,Country)
 livesIn(x,z)
Combine soft and hard constraints
No longer regular MaxSat
Constrained (weighted) MaxSat instead
hasAdvisor(x,y)  hasAdvisor(x,z)  y=z
Generalize to other forms of constraints:
Hard constraint
Soft constraint
hasAdvisor(x,y) 
graduatedInYear(x,t) 
graduatedInYear(y,s)
 s < t
firstPaper(x,p) 
firstPaper(y,q) 
author(p,x)  author(p,y) 
inYear(p) > inYear(q)+5years
 hasAdvisor(x,y)[0.6]
Datalog-style grounding
(deductive & potentially recursive soft rules)
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Deductive Grounding (SLD Resolution/Datalog)
Answers (derived facts):
livesIn(Bill, Arkansas)
livesIn(Bill, New_York)
Query
livesIn(Bill, ?x)
\/
F1
…
R2
R3
/\
X
F3
\/
R1
X
R1
R2
F2
R3
RDF Base Facts
X
F1: marriedTo(Bill, Hillary)
F2: represents(Hillary, New_York)
F3: governorOf(Bill, Arkansas)
First-Order Rules (Horn clauses)
R1: livesIn(?x, ?y) :- marriedTo(?x, ?z), livesIn(?z, ?y)
R2: livesIn(?x, ?y) :- represents(?x, ?y)
R3: livesIn(?x, ?y) :- governorOf(?x, ?y)
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URDF: Reasoning Example
KB:
Base Facts
type[1.0]
Computer
Scientist
Rules
type[1.0]
hasAdvisor(x,y) 
worksAt(y,z)
 graduatedFrom(x,z)
type[1.0]
hasAdvisor[0.8]
Jeff
hasAdvisor[0.7]
Surajit
graduatedFrom
graduatedFrom
[0.6]
[?]
[0.4]
David
graduatedFrom[0.9]
graduatedFrom(x,y) 
graduatedFrom(x,z)
 x=z
graduatedFrom[?]
graduatedFrom[0.7]
worksAt[0.9]
Stanford
Princeton
type[1.0]
type[1.0]
University
Derived Facts
gradFr(Surajit,Stanford)
gradFr(David,Stanford)
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URDF: CNF Construction & MaxSat Solving
[Theobald,Sozio,Suchanek,Nakashole: MPII Tech-Report‘10]
Query
graduatedFrom(?x,?y)
1) Deductive Grounding
CNF
(graduatedFrom(Surajit, Stanford) 
graduatedFrom(Surajit, Princeton)) 
 (graduatedFrom(David, Stanford) 
graduatedFrom(David, Princeton))

 (hasAdvisor(Surajit, Jeff) 
worksAt(Jeff, Stanford) 
graduatedFrom(Surajit, Stanford)) 0.4
 (hasAcademicAdvisor(David, Jeff) 
worksAt(Jeff, Stanford) 
graduatedFrom(David, Stanford))
0.4







worksAt(Jeff, Stanford)
hasAdvisor(Surajit, Jeff)
hasAdvisor(David, Jeff)
graduatedFrom(Surajit, Princeton)
graduatedFrom(Surajit, Stanford)
graduatedFrom(David, Princeton)
graduatedFrom(David, Stanford)
0.9
0.8
0.7
0.6
0.7
0.9
0.0
– Yields only facts and rules which
are relevant for answering the
query (dependency graph D)
2) Boolean Formula in CNF
consisting of
– Grounded hard rules
– Grounded soft rules (weighted)
– Base facts (weighted)
3) Propositional Reasoning
– Compute truth assignment for
all facts in D such that the sum of
weights is maximized
 Compute “most likely” possible
world
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URDF: Lineage & Possible Worlds
Query
graduatedFrom(Surajit,?y)
0.7x(1-0.888)=0.078
graduatedFrom
(Surajit,
Princeton)
0.7
1) Deductive Grounding
– Same as before, but trace
lineage of query answers
(1-0.7)x0.888=0.266
graduatedFrom
(Surajit,
Stanford)
2) Lineage DAG (not CNF!)
consisting of
1-(1-0.72)x(1-0.6)
=0.888

\/
0.8x0.9
=0.72
graduatedFrom
(Surajit,
Princeton)[0.7]
0.8
hasAdvisor
(Surajit,Jeff)[0.8]
/\
– Grounded hard rules
– Grounded soft rules
– Base facts
plus: derivation structure
0.6
graduatedFrom
(Surajit,
Stanford)[0.6]
0.9
worksAt
(Jeff,Stanford)[0.9]
3) Probabilistic Inference
– Marginalization:
aggregate probabilities of all
possible worlds where the
answer is “true”
– Drop “impossible worlds”
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Classes & Complexities
FOL
Grounding first-order
Horn formulas (Datalog)
OWL-DL/lite
OWL
Horn
– Decidable
– EXPTIME-complete, PSPACE-complete
(including recursion, but in P w/o recursion)
Max-Sat (Constrained & Weighted)
– NP-complete
Probabilistic inference in graphical models
– #P-complete
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Monte Carlo Simulation (I)
[Karp,Luby,Madras: J.Alg.’89]
Boolean formula:
F = X1X2  X1X3  X2X3
Naïve sampling:
cnt = 0
repeat N times
randomly choose X1, X2, X3  {0,1}
if F(X1, X2, X3) = 1
then cnt = cnt+1
P = cnt/N
May be very big
return P /* Pr'(F) */
for small Pr(F)
Theorem: If N ≥ (1/ Pr(F)) × (4 ln(2/d)/e2) then:
Pr[ | P/Pr(F) - 1 | > e ] < d
X1X2
X1X3
X2X3
Zero/One-estimator
theorem
Works for any F
(not in PTIME)
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Monte Carlo Simulation (II)
Boolean formula in DNF:
[Karp,Luby,Madras: J.Alg.’89]
F = C1  C2  . . .  Cm
Improved sampling:
cnt = 0;
S = Pr(C1) + … + Pr(Cm)
repeat N times
randomly choose i  {1,2,…, m}, with prob. Pr(Ci)/S
randomly choose X1, …, Xn  {0,1} s.t. Ci = 1
if C1=0 and C2=0 and … and Ci-1= 0
then cnt = cnt+1
P = cnt/N
Now it’s better
return P /* Pr'(F) */
Theorem: If N ≥ (1/m) × (4 ln(2/d)/e2) then:
Pr[ |P/Pr(F) - 1| > e ] < d
Only for F in DNF
in PTIME
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Learning “Soft” Rules
Extend Inductive Logic Programming (ILP) techniques to
large and incomplete knowledge bases
Goal: learn livesIn(?x,?y)  bornIn(?x,?y)
livesIn(x,z)
livesIn(x,y)
Positive Examples
livesIn(?x,?y)  bornIn(?x,?y)
Li
Negative Examples
bornIn(x,y)
Background knowledge
Li
 livesIn(?x,?y)  bornIn(?x,?y)
 livesIn(?x,?z)
Software tools:
alchemy.cs.washington.edu
http://www.doc.ic.ac.uk/~shm/progol.html
http://dtai.cs.kuleuven.be/ml/systems/claudien
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More Variants of Consistency Reasoning
• Propositional Reasoning
– Constrained Weighted MaxSat solver
• Lineage & Possible Worlds (independent base facts)
– Monte Carlo simulations (Luby-Karp)
• First-Order Logic & Probabilistic Graphical Models
– Markov Logic (currently via interface to Alchemy*)
[Richardson & Domingos: ML’06]
– Even more general: Factor Graphs
[McCallum et al. 2008]
– MCMC sampling for probabilistic inference
*Alchemy – Open-Source AI: http://alchemy.cs.washington.edu/
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Experiments
•
•
•
YAGO Knowledge Base: 2 Mio entities, 20 Mio facts
Basic query answering: SLD grounding & MaxSat solving of 10 queries over 16 soft
rules (partly recursive) & 5 hard rules (bornIn, diedIn, marriedTo, …)
Asymptotic runtime checks: runtime comparisons for synthetic soft rule expansions
• URDF: SLD grounding & MaxSat
solving
|C| - # literals in soft rules
|S| - # literals in hard rules
• URDF vs. Markov Logic (MAP
inference & MC-SAT)
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French Marriage Problem (Revisited)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Facts in KB:
1: marriedTo
(Hillary, Bill)
2: marriedTo
(Carla, Nicolas)
3: marriedTo
(Angelina, Brad)
validFrom (2, 2008)
New fact candidates:
4:
5:
6:
7:
8:
marriedTo (Cecilia, Nicolas)
marriedTo (Carla, Benjamin)
marriedTo (Carla, Mick)
divorced (Madonna, Guy)
domPartner (Angelina, Brad)
validFrom (4, 1996)
validFrom (5, 2010)
validFrom (6, 2006)
validFrom (7, 2008)
validUntil (4, 2007)
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Challenge: Temporal Knowledge Harvesting
For all people in Wikipedia (100,000‘s) gather all spouses,
incl. divorced & widowed, and corresponding time periods!
>95% accuracy, >95% coverage, in one night!
Consistency constraints are potentially helpful:
• functional dependencies: {husband, time}  {wife, time}
• inclusion dependencies: marriedPerson  adultPerson
• age/time/gender restrictions: birthdate +  < marriage < divorce
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Difficult Dating
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(Even More Difficult)
Implicit Dating
vague dates
relative dates
narrative text
relative order
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TARSQI: Extracting Time Annotations
http://www.timeml.org/site/tarsqi/
[Verhagen et al: ACL‘05]
Hong Kong is poised to hold the first election in more than half <TIMEX3 tid="t3"
TYPE="DURATION" VAL="P100Y">a century</TIMEX3> that includes a democracy
advocate seeking high office in territory controlled by the Chinese government in Beijing. A prodemocracy politician, Alan Leong, announced <TIMEX3 tid="t4" TYPE="DATE"
VAL="20070131">Wednesday</TIMEX3> that he had obtained enough nominations to
appear on the ballot to become the territory’s next chief executive. But heextraction
acknowledged that
he had no chance of beating the Beijing-backed incumbent, Donald Tsang, who is seeking reerrors!
election. Under electoral rules imposed by Chinese officials, only 796 people on the election
committee – the bulk of them with close ties to mainland China – will be allowed to vote in the
<TIMEX3 tid="t5" TYPE="DATE" VAL="20070325">March 25</TIMEX3>
election. It will be the first contested election for chief executive since Britain returned Hong
Kong to China in <TIMEX3 tid="t6" TYPE="DATE" VAL="1997">1997</TIMEX3>.
Mr. Tsang, an able administrator who took office during the early stages of a sharp economic
upturn in <TIMEX3 tid="t7" TYPE="DATE" VAL="2005">2005</TIMEX3>, is
popular with the general public. Polls consistently indicate that three-fifths of Hong Kong’s
people approve of the job he has been doing. It is of course a foregone conclusion – Donald
Tsang will be elected and will hold office for <TIMEX3 tid="t9" beginPoint="t0"
endPoint="t8“
TYPE="DURATION"
VAL="P5Y">another
five
years
</TIMEX3>, said Mr. Leong, the former chairman of the Hong Kong Bar Association.
23
13 Relations between Time Intervals
[Allen, 1984; Allen & Hayes, 1989]
A Before B
B After A
A Meets B
B MetBy A
A
A Overlaps B
B OverlappedBy A
A
A Starts B
B StartedBy A
A During B
B Contains A
A Finishes B
B FinishedBy A
A Equal B
A
B
B
B
A
B
A
B
A
B
A
B
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Possible Worlds in Time (I)
[Wang,Yahya,Theobald: VLDB/MUD Workshop ‘10]
Derived
Facts

teamMates(Beckham,
Ronaldo,T3)
State
playsFor(Beckham, Real, T1)
 playsFor(Ronaldo, Real, T2)
 overlaps(T1,T2)
0.36
0.16
0.08
‘03
0.4
Base
Facts
0.6
‘04
0.12
‘05
‘07
1.0
0.1
0.2
0.4
0.9
0.2
‘05
‘07
‘03
playsFor(Beckham,Real)
‘00 ‘02
‘07
‘04 ‘05
playsFor(Ronaldo,Real)
State Relation
State Relation
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Possible Worlds in Time (II)
[Wang,Yahya,Theobald: VLDB/MUD Workshop ‘10]
Derived
Facts
won(Beckham,
ChampionsL,T3)

Event
playsFor(Beckham, United, T1)
 wonCup(United, ChampionsL,T2)
 overlaps(T1,T2)
0.54
0.30
0.060.12 0.06
‘96
0.12
‘98 ‘99 ‘00 ‘01
Non-independent
Independent
• Closed and complete representation model (incl. lineage)
 Stanford Trio project [Widom: CIDR’05, Benjelloun et al: VLDB’06]
0.6
0.9
0.5
1.0
• Interval computation
remains linear in the
number0.2of bins
0.20.30.1
0.3
• Confidence
computation
Base
‘98
‘02 per bin is #P-complete
‘95
‘96 ‘98 ‘99 ‘00 ‘01
Facts  In
playsFor(Beckham,
wonCup(United,
ChampionsLeague)
general requires United)
possible-worlds-based
sampling
State
Event
techniques
(Luby-Karp, Gibbs sampling, etc.)
26
Agenda
– URDF: Reasoning in Uncertain Knowledge Bases
•
•
•
•
Resolving uncertainty at query-time
Lineage of answers
Propositional vs. probabilistic reasoning
Temporal reasoning extensions
– UViz: The URDF Visualization Frontend
• Demo!
27
UViz: The URDF Visualization Engine
• UViz System
Architecture
– Flash client
– Tomcat server (JRE)
– Relational backend
(JDBC)
– Remote Method
Invocation & Object
Serialization (BlazeDS)
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UViz: The URDF Visualization Engine
Demo!
29