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Believe It or Not – Adding belief annotations - PPT Presentation

to databases Wolfgang Gatterbauer Magda Balazinska Nodira Khoussainova and Dan Suciu University of Washington httpdbcswashingtonedubeliefDB August 25 VLDB 2009 2 Highlevel overview ID: 651350

belief alice uid sid alice belief sid uid species bob placid lake location date black alice

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Slide1

Believe It or Not – Adding belief annotations to databases

Wolfgang Gatterbauer, Magda Balazinska, Nodira Khoussainova, and Dan SuciuUniversity of Washingtonhttp://db.cs.washington.edu/beliefDB/

August 25, VLDB 2009Slide2

2

High-level overviewDBMS: manage consistent dataApplications need inconsistent DMScientific databasesInternet community databasesCommunity DBMS: manage inconsistent viewsThis work: Belief databasesmanage data and curationgrounded in modal and default logicimplemented on top of relational modelreason: disagreement !Slide3

3Agenda

Motivating exampleLogic foundations Relational implementationDiscussionSlide4

Observations

id

uid

species

date

location

comment

2

Alice

Crow

06-14-08

Lake Placid

found feathers

4

Motivating application

NatureMapping project

(http://depts.washington.edu/natmap/)

volunter contribute animal observations

one person curates the database

Sightings (S)

siduidspeciesdatelocations2AliceCrow06-14-08Lake Placid

Comments (C)cidcommentsidc1found featherss2

problem: does not scale!Slide5

Alice

Bob5

1. Distinct database instances

S

sid

uid

species

date

location

s2

Alice

Raven

06-14-08

Lake Placid

S

sid

uid

species

date

location

s2AliceCrow06-14-08Lake PlacidD1: Belief worlds: individually consistent, mutually possibly inconsistentSlide6

Alice

Bob

6

1. Distinct database instances

S

sid

uid

species

date

location

s2

Alice

Raven

06-14-08

Lake Placid

S

sid

uid

species

date

locations2AliceCrow06-14-08Lake PlacidBeliefSQLinsert into BELIEF ‘Alice’ Sightingsvalues (‘s2’,‘Alice’,‘Crow’,’06-14-08’,‘Lake Placid’)select U2.name, S1.species, S2.speciesfrom Users as U, BELIEF ‘Alice’ Sightings as S1, BELIEF U.uid Sightings as S2,where S1.sid = S2.sidand S1.species <> S2.speciesQ: Who believes something different than Alice and what?A: {(‘Bob’, ‘Crow’, ‘Raven’)}

I: Alice believes that she saw a crow.insert into BELIEF ‘Bob’ Sightingsvalues (‘s2’,‘Alice’,‘Raven’,’06-14-08’,‘Lake Placid’)I: Bob believes that she actually saw a raven.Slide7

Alice

Bob7

2. Open world assumption

S

sid

uid

species

date

location

s2

Alice

Raven

06-14-08

Lake Placid

S

sid

uid

species

date

location

s2AliceCrow06-14-08Lake PlacidCarolSsiduidspeciesdate

locations2AliceCrow06-14-08Lake Placids2Alice

Raven

06-14-08

Lake Placid

D2: Model incomplete knowledge with exlicit negative beliefs

Adapted key constraints !Slide8

Alice

Bob8

2. Open world assumption

S

sid

uid

species

date

location

s2

Alice

Raven

06-14-08

Lake Placid

S

sid

uid

species

date

location

s2AliceCrow06-14-08Lake PlacidCarolSsiduidspeciesdate

locations2AliceCrow06-14-08Lake Placids2Alice

Raven

06-14-08

Lake Placid

I: Carol does not believe that Alice saw a crow

nor a raven.

insert into

BELIEF

‘Carol’ not

Sightings

values (‘s2’,‘Alice’,‘Crow’,’06-14-08’,‘Lake Placid’)

insert into

BELIEF

‘Carol’ not

Sightings

values (‘s2’,‘Alice’,‘Raven’,’06-14-08’,‘Lake Placid’)Slide9

Alice

Bob9

2. Open world assumption

S

sid

uid

species

date

location

s2

Alice

Raven

06-14-08

Lake Placid

S

sid

uid

species

date

location

s2AliceCrow06-14-08Lake PlacidCarolSsiduidspeciesdate

locations2AliceCrow06-14-08Lake Placids2Alice

Raven

06-14-08

Lake Placid

Q: Who disagrees with a sighting from

‘06-14-08’ that Alice believes?

A: {(‘Bob’, ‘Crow’), (‘Carol’, ‘Crow’)}

select U.name, S1.species

from

Users as U

,

BELIEF

‘Alice’

Sightings as S1,

BELIEF

U.uid not

Sightings as S2

where S1.sid = S2.sid

and S1.uid = S2.uid

and S1.species = S2.species

and S1.date = ‘06-14-08’

and S2.date = ‘06-14-08’

and S1.location = S2.locationSlide10

Bob

Alice

Alice

Bob

10

3. Higher-order beliefs

C

cid

comment

sid

c1

purple-black feathers

s2

C

cid

comment

sid

c1

plain

black featherss2Ssiduidspeciesdatelocations2AliceRaven06-14-08Lake Placid

Ssiduidspeciesdatelocations2Alice

Crow

06-14-08

Lake Placid

D3: Beliefs about other user’s beliefs: allow discussion between usersSlide11

Bob

Alice

Alice

Bob

11

3. Higher-order beliefs

C

cid

comment

sid

c1

purple-black feathers

s2

C

cid

comment

sid

c1

plain

black featherss2Ssiduidspeciesdatelocations2AliceRaven06-14-08Lake Placid

Ssiduidspeciesdatelocations2Alice

Crow

06-14-08

Lake Placid

I: According to Bob, Alice believes that the

feathers of the sighted animal were plain black.

insert into

BELIEF

‘Bob’

BELIEF

‘Alice’

Comments

values (‘c1’, ‘plain black feathers’, ‘s2’)Slide12

Bob

Alice

Alice

Bob

12

3. Higher-order beliefs

C

cid

comment

sid

c1

purple-black feathers

s2

C

cid

comment

sid

c1

plain

black featherss2Ssiduidspeciesdatelocations2AliceRaven06-14-08Lake Placid

Ssiduidspeciesdatelocations2Alice

Crow

06-14-08

Lake Placid

select C1.cid, C1.comment

from

BELIEF

‘Bob’

BELIEF

‘Alice’

Comments as C1,

BELIEF

‘Bob’ not

Comments as C2

where C1.cid = C2.cid

and C1.comment = C2.comment

and C1.sid = C2.sid

Q: Which comments does Alice believe according

to Bob, which he does not believe himself?

A: {(‘c1’,‘plain-black feathers’)}Slide13

Bob

Alice

Alice

Bob

13

3. Higher-order beliefs

C

cid

comment

sid

c1

purple-black feathers

s2

C

cid

comment

sid

c1

plain

black featherss2Ssiduidspeciesdatelocations2AliceRaven06-14-08

Lake PlacidSsiduidspeciesdatelocations2

Alice

Crow

06-14-08

Lake Placid

select U.name, C1.sid, C1.comment

from

Users as U,

BELIEF

U.uid

BELIEF

‘Alice’

Comments as C1,

BELIEF

U.uid not

Comments as C2

where C1.cid = C2.cid

and C1.comment = C2.comment

and C1.sid = C2.sid

Q: Which comments does Alice believe according

to somebody, which (s)he does not believe themself?

A: {(‘Bob’, ‘c1’, ‘plain-black feathers’)}Slide14

C

cid

comment

sid

c1

purple-black feathers

s2

Bob

Alice

Alice

Bob

C

cid

comment

sid

c1

plain

black

feathers

s2Ssiduidspeciesdatelocations2AliceRaven06-14-08Lake Placid

144. Message board assumptionSsiduidspeciesdatelocations2

Alice

Crow

06-14-08

Lake Placid

S

sid

uid

species

date

location

s2

Alice

Crow

06-14-08

Lake Placid

D4: Default assumption: models a trusting attitude & avoids repeated insertsSlide15

15

4. Message board assumption

Alice

Bob

Bob

Alice

C

cid

comment

sid

c1

purple-black feathers

s2

C

cid

comment

sid

c1

plain

black featherss2Ssiduidspeciesdatelocations2AliceRaven06-14-08Lake Placid

Ssiduidspeciesdatelocations2Alice

Crow

06-14-08

Lake Placid

S

sid

uid

species

date

location

s2

Alice

Crow

06-14-08

Lake Placid

Q: Which animal sightings does Alice believe

according to Bob, which he does not

believe himself?

select S1.sid, S1.species

from

BELIEF

‘Bob’

BELIEF

‘Alice’

Sightings as S1,

BELIEF

‘Bob’ not

Sightings as S2

where S1.sid = S2.sid

and S1.uid = S2.uid

and S1.species = S2.species

and S1.date = S2.date

and S1.location = S2.location

A: {(‘s2’, ‘Crow’)}Slide16

16What we have seen so far

4 Design decisions for Belief Database modelDistinct belief worldsOpen world assumption (OWA)Higher-order beliefsMessage board assumptionBeliefSQLSQL + ‘BELIEF’ (+ ‘not’)Slide17

17Agenda

Motivating exampleLogic foundations Relational implementationDiscussionSlide18

Bob

AliceBob18Logic foundations: Belief statements

Carol

Alice

Carol

insert into

BELIEF

‘Alice’

S

values (‘s2’, ‘Alice’, ‘Crow’,…)

i:

Alice

S

+

(‘s2’,‘Alice’,‘Crow’,…)belief statement = ☐w t

s

relational tuple (t)

sign (s)

modal operator

& belief path (w)BobCarolAliceBob………………AliceεBelief database D = {1, …, n}Alice

AliceSsiduidspecies…s2AliceCrow

“annotation of

ground tuple”Slide19

19

Logic foundations: Entailment

Carol

Carol

Alice

S

sid

uid

species

s2

Alice

Crow

Bob

Carol

Alice

Bob

………ε1=☐Alice S+(…‘Crow’,…)BobS

siduidspecies…s2AliceCrow…

Alice

Bob

Alice

Alice

select *

from

BELIEF

‘Bob’

BELIEF

‘Alice’

S

D

Bob

A

lice

S

+

(…‘Crow’,…)

Bob

Alice

Alice

One belief annotation:

More than one entailed belief:

D =

{

1

}Slide20

20

Logic foundations: Message board assumption

If D ☐

w t

s

Message board assumption

then

D

u

w

t

s

and ☐uw ts consistent with D : ☐u ☐u  Default logicDExplicit beliefs(annotations)DEntailed beliefs(extension)

D \ D

Implicit beliefs

(assumptions)

non-monotonic reasoning !

belief database “contains” more than the explicit belief annotations !Slide21

21

“Semi-formal” problem statementi1: 1i2: 2

...in:

n

Belief statements

Message board

assumption

 :

u

u

 INPUTOUTPUTAdaptedkey constraintsD  ?D ☐w1…wd R+(x1,…x

l) ?

Belief Conjunctive Queries (BCQ)

q(x) :

☐w Ri+(xi)q(x) :− ☐w1R1s1(x1), …, ☐wgRgsg(xg)Slide22

22Agenda

Motivating exampleLogic foundations Relational implementationDiscussionSlide23

{

s11−,s12−,s22+,c22+}

{s11+,s2

1+,

c11+

,

c2

1

+

}

{s1

1

+

}

{s1

1+,s21+,c11+}23Canonical Kripke structurei1: s11+i2: ☐Bob s11−i3: ☐Bob s12−i

4: ☐Alice s2

1+

i

5: ☐Alice

c11+i6: ☐Bob s22+i7: ☐BobAlice c21+i8: ☐Bob c22+Belief statements*Message board assumption : ☐i ☐i  AliceBobBobCarolBobCarolAlice

#1#0#2* Running example from the paper

Carol

Carol

#3Slide24

24Relational representation

Comments_INTERNAL

tid

cid

comment

sid

c1.1

c1

found feathers

s2

c2.1

c2

plain black feathers

s2

c2.2

c2

purple-black feathers

s2

Sightings_INTERNAL

tid

siduidspeciesdatelocation

s1.1s1CarolBald eagle06-14-08Lake Forests1.2s1Carol

Fish eagle

06-14-08

Lake Forest

s2.1

s2

Alice

Crow

06-14-08

Lake Placid

s2.2

s2

Alice

Raven

06-14-08

Lake Placid

Sightings_V

wid

tid

sid

s

e

#0

s1.1

s1

+

y

#1

s1.1

s1

+

n

#1

s2.1

s2

+

y

#2

s1.1

s1

y

#2

s1.2

s1

y

#2

s2.2

s2

+

y

#3

s1.1

s1

+

n

#3

s2.1

s2

+

n

Comments_V

wd

tid

cid

s

e

#1

c1.1

c1

+

y

#2

c2.2

c2

+

y

#3

c1.1

c1

+

n

#3

c2.1

c2

+

y

E

wid1

uid

wid2

#0

Alice

#1

#0

Bob

#2

#0

Carol

#0

#1

Bob

#2

#1

Carol

#0

#2

Alice

#3

#2

Carol

#0

#3

Bob

#2

#3

Carol

#0

D

wid

d

#0

0

#1

1

#2

1

#3

2

S

wid1

wid2

#1

#0

#2

#0

#3

#1Slide25

25Example Translation of a Belief CQ (BCQ)

BeliefSQLselect U.name, S1.speciesfrom Users as U, BELIEF ‘Alice’ Sightings as S1, BELIEF U.uid not Sightings as S2where S1.sid = S2.sidand S1.uid = S2.uidand S1.species = S2.species

and S1.date = ‘06-14-08’and S2.date = ‘06-14-08’and S1.location = S2.location

Q: Who disagrees with a sighting from ’06-14-08’ that Alice believes?

select E1.uid as uid1, V.tid, V.sid, R.uid, R.species, R.date, R.location, V.sinto T2

from E as E1, Sightings_V as V, Sightings_STAR as R

where E1.wid1=0

and V.wid=E1.wid2

and V.tid=R.tid

and E1.uid='1';

 

select E1.uid as uid1, V.tid, V.sid, R.uid, R.species, R.date, R.location, V.s

into T1

from E as E1, Sightings_V as V, Sightings_STAR as R

where E1.wid1=0

and V.wid=E1.wid2and V.tid=R.tid; select T1.uid1, T2.speciesfrom T1 as T1, T2 as T2where T1.sid=T2.sidand ((T1.s=0 and T1.uid=T2.uid and T1.species=T2.species and T1.date='6-14-08' and T1.location=T2.location) or (T1.s=1 and (T1.uid<>T2.uid or T1.species<>T2.species or T1.date<>'6-14-08' or T1.location<>T2.location)))and T2.s=1and T2.date='6-14-08'; drop table T2;drop table T1;Translation into SQLq(x,y) :− ☐Alice S+(u,v,y,‘06-14-08’,z), ☐x S−(u,v,y,‘06-14-08’,z)Slide26

26Agenda

Motivating exampleLogic foundations Relational implementationDiscussionSlide27

27Experiments

Relative overhead ρ :=|R*|n

ρ = O(m

dmax

)

m … #users

d

max

… maximum

depth of belief

annotation

In theory: e.g. 100 users, max. depth 2

Experiments:

ρ

10,000ρ  21 – 1,009Size not limitation of semantics, but of relational implementation!SizeTimeDepends on type of query (3 types in paper)Experiments on 10,000 annotations (ρ =22.4):Considerable speed-up to come!Q1: ~0.1 sQ2: ~0.4 sQ3: ~4.5 sSlide28

28Inspirations and related work (excerpt)

AnnotationsBuneman et al. [ICDT 2001 / ICDT 2007]Bhagwat et al. [VLDBJ 2005], Geerts et al. [ICDE 2006]Srivastava & Velegrakis [SIGMOD 2007]Modal logicFagin et al. [1995] Calvanese et al. [IS 2008]Nguyen [LJ-IGPL 2008]Uncertain / incomplete informationSarma et al. [ICDE 2006]Green & Tannen [IEEE Data Eng. 2006]Dalvi & Suciu [PODS 2007] Inconsistency / key violationsArenas et al. [PODS 1999]Fuxman et al. [SIGMOD 2005]Peer-to-peer computing / collaborative data sharingBernstein et al. [WebDB 2002]Ives et al. [SIGMOD record 2008]Slide29

29Conclusions

Proposed BELIEF databasesGoal: manage, curate inconsistent dataImplementationLogical foundationsRelational translationCurrent workmaking it compact and fastSlide30

30

BACKUPSlide31

31Relative overhead of relational representation

Distribution of belief path depths (Pr[k=x])Slide32

32Query types and execution timesSlide33

33Belief Conjunctive Queries (BCQ)Slide34

34

Revisiting the semantics / the userBELIEF ’Alice’ (…,’eagle’,…)-> ’Alice’ASSERTS (…,’eagle’,…)

BELIEF ’Bob’ BELIEF ’Alice’ (…,’black feathers’,…)

-> ’Bob’SUGGESTS that the ASSUMPTION (…,’black feathers’,…) has led ‘Alice’ to her original observation

Standard relational model

Conflicts in belief worlds:

OWA, keys, ML, DA

-

> Structured discourse

(1) SQL

(2) BeliefSQL

(3) ?