IR Models based on Predicate Logic - uni-due.de · Propositional vs. Predicate Logic IR and Databases The Logic View Retrieval DB: given query q, nd objects o with o !q IR: given

IR Models based on Predicate Logic


Norbert Fuhr

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The logical view on IR

IR as InferenceIR as uncertain inferencePropositional vs. Predicate Logic

Disjoint eventsRelational BayesProbabilistic rules



IR as Inference

The logical view on IRIR as inference

q - queryd – documentretrieval:search for documents which imply the query: d → q

Example: classical IR:d = {t1, t2, t3}q = {t1, t3}retrieval: q ⊂ d ?

logical view:d = t1 ∧ t2 ∧ t3

q = t1 ∧ t3

retrieval: d → q ?

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IR as Inference

advantage of inference-based approach:step from term-based to knowledge-based retrievale.g. easy incorporation of additional knowledgeexample:d : ’squares’q: ’rectangles’thesaurus: ’squares’ → ’rectangles’⇒: d → q

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IR as uncertain inference

IR as uncertain inference

d : ’quadrangles’q: ’rectangles’⇒ uncertain knowledge required

’quadrangles’0.3→ ’rectangles’

[Rijsbergen 86]:IR as uncertain inferenceRetrieval =estimate probability P(d → q) = P(q|d)

t1 t4

t2 t5

t3 t6d

q

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Propositional vs. Predicate Logic

Limitations of propositional logic:

conventional indexing (based on propositional logic): d = {tree,house}query: Is there a picture with a tree on the left of the house?⇒ query cannot be expressed in propositional logic

predicate logic:

d: tree(t1). house(h1). left(h1,t1).

?- tree(X) & house(Y) & left(X,Y).

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Relational Structures: Datalog

Datalog program: finite set of rules each expressing a conjunctivequery

t(X1, ...,Xk) : −r1(U11, . . . ,U1m1), . . . , rn(Un1, . . . ,Unmn)

where each variable Xi occurs in the body of the rule (this way,every rule is safe).

woman(X) :- person(X), sex(X,female).

path(X,Y) :- link(X,Y).

path(X,Z):-link(X,Y), path(Y,Z).

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Datalog rules

t(X1, ...,Xk) : −r1(U11, . . . ,U1m1), . . . , rn(Un1, . . . ,Unmn)

corresponds to the logical formula

∀X1 . . . ∀Xk∀U11 . . . ∀Unmn

t(X1, ...,Xk) ∧ ¬r1(U11, . . . ,U1m1) ∧ . . . ∧ ¬rn(Un1, . . . ,Unmn)

t(X1, ..., xk) is called the head andr1(U11, . . . ,U1m1), ..., rn(Un1, . . . ,Unmn) the body.

A formula without a head is also called a fact

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Datalog Properties

horn predicate logic

no functions

restricted forms of negation allowed

t(X1, ...,Xk) : −r1(U11, . . . ,U1m1), ...,¬rn(Un1, . . . ,Unmn)

rules may be recursive (head predicate may occur in the body)

r(X ,Y ) : −l(X ,Z ), r(Z ,Y )

sound and complete evaluation algorithms

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IR and DatabasesThe Logic View

Retrieval

DB: given query q, find objects o with o → q

IR: given query q, find documents d with high values ofP(d → q)

DB is a special case of IR!(in a certain sense)

This section: Focusing on the logic view

Inference

Vague predicates

Query language expressiveness

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IR and DatabasesThe Logic View

Retrieval

DB: given query q, find objects o with o → q

IR: given query q, find documents d with high values ofP(d → q)

DB is a special case of IR!(in a certain sense)

This section: Focusing on the logic view

Inference

Vague predicates

Query language expressiveness

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Inference

IR with the Relational ModelThe Probabilistic Relational ModelInterpretation of probabilistic weightsExtensions



Inference

IR with the Relational Model

Relational ModelProjection

indexDOCNO TERM

1 ir1 db2 ir3 db3 oop4 ir4 ai5 db5 oop

topic

irdboopai

Projection: what is the collection about?topic(T) :- index(D,T).

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Inference


Relational ModelSelection

indexDOCNO TERM


aboutir

124

Selection: which documents are about IR?aboutir(D) :- index(D,ir).

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Inference


Relational ModelJoin

indexDOCNO TERM


authorDOCNO NAME

1 smith2 miller3 johnson4 firefly4 bradford5 bates

irauthor

smithmillerfireflybradford

Join: who writes about IR?irauthor(A):- index(D,ir) & author(D,A).

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Inference


Relational ModelUnion

indexDOCNO TERM


irordb

12345

Union: which documents are about IR or DB?irordb(D) :- index(D,ir).

irordb(D) :- index(D,db).

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Inference


Relational ModelDifference

indexDOCNO TERM


irnotdb

24

Difference: which documents are about IR, but not DB?irnotdb(D) :- index(D,ir) & not(index(D,db)).

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Inference

The Probabilistic Relational Model


[Fuhr & Roelleke 97] [Suciu et al 11]

indexβ DOCNO TERM

0.8 1 IR0.7 1 DB0.6 2 IR0.5 3 DB0.8 3 OOP0.9 4 IR0.4 4 AI0.8 5 DB0.3 5 OOP

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Inference




indexβ DOCNO TERM


Which documents are about DB?aboutdb(D) :- index(D,db).

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Inference




indexβ DOCNO TERM


aboutdb0.7 10.5 30.8 5


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Inference




indexβ DOCNO TERM


aboutdb0.7 10.5 30.8 5

aboutirdb0.8*0.7 1


Which documents are about IR and DB?aboutirdb(D) :- index(D,ir) & index(D,db). 17 / 85


Inference


Extensional vs. intensional semantics

doctermβ DOC TERM

0.9 d1 ir0.5 d1 db

linkβ S T

0.7 d2 d1

about(D,T) :- docTerm(D,T).

about(D,T) :- link(D,D1) & about(D1,T)

q(D) :- about(D,ir) & about(D,db).

Extensional semantics:weight of derived fact as function of weights of subgoalsP(q(d2)) = P(about(d2,ir)) · P(about(d2,db)) =

(0.7 · 0.9) · (0.7 · 0.5)

Problem

“improper treatment of correlated sources of evidence” [Pearl 88]→ extensional semantics only correct for tree-shaped inferencestructures

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Inference



doctermβ DOC TERM

0.9 d1 ir0.5 d1 db

linkβ S T

0.7 d2 d1





(0.7 · 0.9) · (0.7 · 0.5)

Problem


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Inference



doctermβ DOC TERM

0.9 d1 ir0.5 d1 db

linkβ S T

0.7 d2 d1





(0.7 · 0.9) · (0.7 · 0.5)

Problem


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Inference


Intensional semantics

weight of derived fact as function of weights of underlying groundfacts

Method: Event keys and event expressions

doctermβ κ DOC TERM

0.9 dT(d1,ir) d1 ir0.5 dT(d1,db) d1 db

linkβ κ S T

0.7 l(d2,d1) d2 d1

?- docTerm(D,ir) & docTerm(D,db).

givesd1 [dT(d1,ir) & dT(d1,db)] 0.9 · 0.5 = 0.45

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Inference







linkβ κ S T

0.7 l(d2,d1) d2 d1



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Inference







linkβ κ S T

0.7 l(d2,d1) d2 d1



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Inference







linkβ κ S T

0.7 l(d2,d1) d2 d1



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Inference


Event keys and event expressions



linkβ κ S T

0.7 l(d2,d1) d2 d1



?- about(D,ir) & about(D,db).

givesd1 [dT(d1,ir) & dT(d1,db)] 0.9 · 0.5 = 0.45d2 [l(d2,d1) & dT(d1,ir) & l(d2,d1) & dT(d1,db)]

0.7 · 0.9 · 0.5 = 0.315

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Inference


Recursion


about(D,T) :- link(D,D1) & about(D1,T).

d3

docterm

linkd1 d2

0.5

0.40.8

0.9

0.5

ir

db

?- about(D,ir)

d1 [dT(d1,ir) | l(d1,d2) & l(d2,d3) & l(d3,d1) &

dT(d1,ir) | ...] 0.900d3 [l(d3,d1) & dT(d1,ir)] 0.720d2 [l(d2,d3) & l(d3,d1) & dT(d1,ir)] 0.288

?- about(D,ir) & about(D,db)

d1 [dT(d1,ir) & dT(d1,db)] 0.450d3 [l(d3,d1) & dT(d1,ir) & l(d3,d1) & dT(d1,db)] 0.360

d2 [l(d2,d3) & l(d3,d1) & dT(d1,ir) & dT(d1,db)] 0.14421 / 85


Inference


Computation of probabilities for event expressions

1 transformation of expression into disjunctive normal form2 application of sieve formula:

simple case of 2 conjuncts: P(a∨ b) = P(a) +P(b)−P(a∧ b)general case:ci – conjunct of event keys

P(c1 ∨ . . . ∨ cn) =n∑

i=1

(−1)i−1∑

1≤j1<...<ji≤n

P(cj1 ∧ . . . ∧ cji ).

exponential complexity

use only when necessary for correctness

see [Dalvi & Suciu 07]

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Inference





P(c1 ∨ . . . ∨ cn) =n∑

i=1

(−1)i−1∑

1≤j1<...<ji≤n

P(cj1 ∧ . . . ∧ cji ).




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Inference





P(c1 ∨ . . . ∨ cn) =n∑

i=1

(−1)i−1∑

1≤j1<...<ji≤n

P(cj1 ∧ . . . ∧ cji ).




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Inference





P(c1 ∨ . . . ∨ cn) =n∑

i=1

(−1)i−1∑

1≤j1<...<ji≤n

P(cj1 ∧ . . . ∧ cji ).




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Inference

Interpretation of probabilistic weights

Possible worlds semantics

0.9 docTerm(d1,ir).

P(W1) = 0.9: {docTerm(d1,ir)}P(W2) = 0.1: {}

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Inference


0.6 docTerm(d1,ir). 0.5 docTerm(d1,db).

Possible interpretations:

I1: P(W1) = 0.3: {docTerm(d1,ir)}P(W2) = 0.3: {docTerm(d1,ir), docTerm(d1,db)}P(W3) = 0.2: {docTerm(d1,db)}P(W4) = 0.2: {}

I2: P(W1) = 0.5: {docTerm(d1,ir)}P(W2) = 0.1: {docTerm(d1,ir), docTerm(d1,db)}P(W3) = 0.4: {docTerm(d1,db)}

I3: P(W1) = 0.1: {docTerm(d1,ir)}P(W2) = 0.5: {docTerm(d1,ir), docTerm(d1,db)}P(W3) = 0.4: {}

probabilistic logic:0.1 ≤ P(docTerm(d1, ir)&docTerm(d1, db)) ≤ 0.5probabilistic Datalog with independence assumptions:P(docTerm(d1, ir)&docTerm(d1, db)) = 0.3

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Inference








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Inference








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Inference

Extensions

Disjoint events

β City State

0.7 Paris France0.2 Paris Texas0.1 Paris Idaho

Interpretation:P(W1) = 0.7: {cityState(paris, france)}P(W2) = 0.2: {cityState(paris, texas)}P(W3) = 0.1: {cityState(paris, idaho)}

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Inference

Extensions

Disjoint events

β City State

0.7 Paris France0.2 Paris Texas0.1 Paris Idaho

Interpretation:P(W1) = 0.7: {cityState(paris, france)}P(W2) = 0.2: {cityState(paris, texas)}P(W3) = 0.1: {cityState(paris, idaho)}

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Inference

Extensions

Relational Bayes

[Roelleke et al. 07]

Role of the relational Bayes: Generation of a probabilistic database

database

Non−probabilistic Bayes

database

Probabilistic

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Inference

Extensions

Relational BayesExample: P(Nationality | City)

nationality and cityNationality City

”British” ”London””British” ”London””British” ”London””Scottish” ”London””French” ”London””German” ”Hamburg””German” ”Hamburg””Danish” ”Hamburg””British” ”Hamburg””German” ”Dortmund””German” ”Dortmund””Turkish” ”Dortmund””Scottish” ”Glasgow”

=⇒Bayes[$City]()

nationality cityP(Nationality|City) Nationality City

0.600 ”British” ”London”0.200 ”Scottish” ”London”0.200 ”French” ”London”0.500 ”German” ”Hamburg”0.250 ”Danish” ”Hamburg”0.250 ”British” ”Hamburg”0.667 ”German” ”Dortmund”0.333 ”Turkish” ”Dortmund”1.000 ”Scottish” ”Glasgow”

1 # P(Nationality | City) :2 nationality city SUM(Nat, City) :−3 nationality and city (Nat, City) | (City) ;

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Inference

Extensions

Relational BayesExample: P(t|d)

termTerm DocId

sailing doc1boats doc1sailing doc2boats doc2sailing doc2east doc3coast doc3sailing doc3sailing doc4boats doc5

p t d space(Term, DocId) :-term(Term, DocId) | (DocId);

P(t|d) Term DocId

0.50 sailing doc10.50 boats doc10.33 sailing doc20.33 boats doc20.33 sailing doc20.33 east doc30.33 coast doc30.33 sailing doc31.00 sailing doc41.00 boats doc5

p t d SUM(Term, DocId) :-term(Term, DocId) | (DocId);

P(t|d) Term DocId

0.50 sailing doc10.50 boats doc10.67 sailing doc20.33 boats doc20.33 east doc30.33 coast doc30.33 sailing doc31.00 sailing doc41.00 boats doc5

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Inference

Extensions

Probabilistic rulesRules for deterministic facts:

0.7 likes-sports(X) :- man(X).

0.4 likes-sports(X) :- woman(X).

man(peter).

Interpretation:P(W1) = 0.7: {man(peter), likes-sports(peter)}P(W2) = 0.3: {man(peter)}

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Inference

Extensions

Probabilistic rulesRules for deterministic facts:

0.7 likes-sports(X) :- man(X).

0.4 likes-sports(X) :- woman(X).

man(peter).

Interpretation:P(W1) = 0.7: {man(peter), likes-sports(peter)}P(W2) = 0.3: {man(peter)}

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Inference

Extensions

Probabilistic rulesRules for uncertain facts:

# gender is disjoint on the first attribute

0.7 l-sports(X) :- gender(X,male).

0.4 l-sports(X) :- gender(X,female).

0.5 gender(X,male) :- human(X).

0.5 gender(X,female) :- human(X).

human(jo).

Interpretation:P(W1) = 0.35: {gender(jo,male), l-sports(jo)}P(W2) = 0.15: {gender(jo,male)}P(W3) = 0.20: {gender(jo,female), l-sports(jo)}P(W4) = 0.30: {gender(jo,female)}

?- l-sports(jo) P(W1) + P(W3) = 0.5530 / 85


Inference

Extensions







human(jo).


?- l-sports(jo) P(W1) + P(W3) = 0.5530 / 85


Inference

Extensions







human(jo).


?- l-sports(jo) P(W1) + P(W3) = 0.5530 / 85


Inference

Extensions

Probabilistic rulesRules for independent events

sameauthor(D1,D2) :- author(D1,X) & author(D2,X).

0.5 link(D1,D2) :- refer(D1,D2).

0.2 link(D1,D2) :- sameauthor(D1,D2).

?? link(D1,D2) :- refer(D1,D2) & sameauthor(D1,D2).

P(l |r), P(l |s) → P(l |r ∧ s)?

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Inference

Extensions

Rules for independent eventsModeling probabilistic inference networks

0.7 link(D1,D2) :- refer(D1,D2) & sameauthor(D1,D2).

0.5 link(D1,D2) :- refer(D1,D2) & not(sameauthor(D1,D2)).

0.2 link(D1,D2) :- sameauthor(D1,D2) & not(refer(D1,D2)).

Probabilistic inference networks,rules define link matrix

refer sameauthor

link

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Vague Predicates


The Logical View on Vague PredicatesVague Predicates in IR and DatabasesProbabilistic Modeling of Vague Predicates


Vague Predicates

Vague PredicatesMotivating Example

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Vague Predicates

Vague PredicatesMotivating Example

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Vague Predicates

The Logical View on Vague Predicates


Current IR systems are based on proposition logic(query term present/absent in document)

Similarity of values not considered

but multimedia IR deals with similarity already

transition from propositional to predicate logic necessary

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Vague Predicates







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Vague Predicates







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Vague Predicates







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Vague Predicates







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Vague Predicates


Vague Predicates in Probabilistic Datalog

[Fuhr & Roelleke 97] [Fuhr 00]

Example: Shopping 45 inch LCD TV

vague predicates as builtin predicates:X ≈ Y

query(D):- Category(D,tv) &

type(D,lcd) & size(D,X) &

≈(X,45)

X ≈ Y

β X Y

0.7 42 450.8 43 450.9 44 451.0 45 450.9 46 450.8 47 45. . . . . . . . .

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Vague Predicates

Vague Predicates in IR and Databases

Data types and vague predicates in IR

Data type: domain + (vague) predicates

Language (multilingual documents) /(language-specific stemming)

Person names / “his name sounds like Jones”

Dates / “about a month ago”

Amounts / “orders exceeding 1 Mio $”

Technical measurements / “at room temperature”

Chemical formulas

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Vague Predicates


Vague Criteria in Fact Databases

”I am looking for a 45-inch LCD TV with

wide viewing angle

high contrast

low price

high user rating”

→ vague criteria are very frequent in end-user querying of factdatabases

→ but no appropriate support in SQL

vague conditions → similar to fuzzy predicates

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Vague Predicates


Vague Criteria in Fact Databases

”I am looking for a 45-inch LCD TV with

wide viewing angle

high contrast

low price

high user rating”

→ vague criteria are very frequent in end-user querying of factdatabases

→ but no appropriate support in SQL

vague conditions → similar to fuzzy predicates

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Vague Predicates

Probabilistic Modeling of Vague Predicates

Probabilistic Modeling of Vague Predicates

[Fuhr 90]

learn vague predicates fromfeedback data

construct feature vector~x(qi , di ) from query value qiand document value di(e.g. relative difference)

apply logistic regression

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Expressiveness


Retrieval Rules, Joins, Aggregations and RestructuringExpressiveness in XML Retrieval


Expressiveness

Retrieval Rules, Joins, Aggregations and Restructuring

ExpressivenessFormulating Retrieval Rules


consider document linking / anchor textabout(D,T) :- link(D1,D),about(D1,T).

consider term hierarchyabout(D,T) :- subconcept(T,T1) & about(D,T1).

field-specific term weighting0.9 docTerm(D,T) :- occurs(D,T,title).

0.5 docTerm(D,T) :- occurs(D,T,body).

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Expressiveness








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Expressiveness








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Expressiveness








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Expressiveness


ExpressivenessJoins

IR authors:

irauthor(N):- about(D,ir) & author(D,N).

Smith’s IR papers cited by Miller

?- author(D,smith) & about(D,ir) &

author(D1,miller) & cites(D,D1).

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Expressiveness


ExpressivenessJoins

IR authors:

irauthor(N):- about(D,ir) & author(D,N).

Smith’s IR papers cited by Miller

?- author(D,smith) & about(D,ir) &

author(D1,miller) & cites(D,D1).

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Expressiveness


ExpressivenessAggregation (1)

Who are the major IR authors?

indexβ DNO TERM

0.9 1 ir0.8 1 db0.6 2 ir0.8 3 ir0.7 3 ai

authorDNO NAME

1 smith2 miller3 smith

irauthor0.98 smith0.6 miller

irauthor(A):- index(D,ir) & author(D,A).

Aggregation through projection!

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Expressiveness




indexβ DNO TERM

0.9 1 ir0.8 1 db0.6 2 ir0.8 3 ir0.7 3 ai

authorDNO NAME


irauthor0.98 smith0.6 miller

irauthor(A):- index(D,ir) & author(D,A).

Aggregation through projection!

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Expressiveness




indexβ DNO TERM

0.9 1 ir0.8 1 db0.6 2 ir0.8 3 ir0.7 3 ai

authorDNO NAME


irauths1.7 smith0.6 miller

Aggregation through summing:

irauth(D,A):- index(D,ir) & author(D,A).

irauths SUM(Name) :- irdbauth(Doc,Name) | (Name)

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Expressiveness

Expressiveness in XML Retrieval


[Fuhr & Lalmas 07]

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Expressiveness



[Fuhr & Lalmas 07]

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Expressiveness


XML structure: 1. Nested Structure

XML document as hierarchicalstructure

Retrieval of elements (subtrees)

Typical query language does notallow for specification of structuralconstraints

Relevance-oriented selection ofanswer elements: return the mostspecific relevant elements

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Expressiveness


XML structure: 2. Named Fields

Reference to elementsthrough field names only

Context of elements isignored(e.g. author of article vs.author of referenced paper)

Post-Coordination may leadto false hits(e.g. author name – authoraffiliation)

Example: Dublin Core<oai dc:dc xmlns:dc=

"http://purl.org/dc/elements/1.1/">

<dc:title>Generic Algebras

... </dc:title>

<dc:creator>A. Smith (ESI),

B. Miller (CMU)</dc:creator>

<dc:subject>Orthogonal group,

Symplectic group</dc:subject>

<dc:date>2001-02-27</dc:date>

<dc:format>application/postscript</dc:format>

<dc:identifier>ftp://ftp.esi.ac.at/pub/esi1001.ps</dc:identifier>

<dc:source>ESI preprints

</dc:source>

<dc:language>en</dc:language>

</oai dc:dc>47 / 85


Expressiveness


XML structure: 3. XPath

/document/chapter[about(./heading, XML) AND

about(./section//*,syntax)]

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Expressiveness


XML structure: 3. XPath

/document/chapter[about(./heading, XML) AND

about(./section//*,syntax)]

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Expressiveness


XML structure: 3. XPath (cont’d)

Full expressiveness for navigation through document tree(+links)

Parent/child, ancestor/descendantFollowing/preceding, following-sibling, preceding-siblingAttribute, namespace

Selection of arbitrary elements/subtrees(but answer can be only a single element of the originatingdocument)

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Expressiveness


XML structure: 4. XQuery

Higher expressiveness, especially for database-like applications:

Joins (trees → graphs)

Aggregations

Constructors for restructuring results

Example: List each publisher and the average price of its books

FOR $p IN distinct(document("bib.xml")//publisher)

LET $a := avg(document("bib.xml")//book[publisher =

$p]/price)

RETURN

<publisher>

<name> $p/text() </name>

<avgprice> $a </avgprice>

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Expressiveness


XML structure: 4. XQuery

Higher expressiveness, especially for database-like applications:

Joins (trees → graphs)

Aggregations

Constructors for restructuring results

Example: List each publisher and the average price of its books

FOR $p IN distinct(document("bib.xml")//publisher)

LET $a := avg(document("bib.xml")//book[publisher =

$p]/price)

RETURN

<publisher>

<name> $p/text() </name>

<avgprice> $a </avgprice>

</publisher>50 / 85


Expressiveness


XML content typing

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Expressiveness


XML content typing: 1. Text<book>

<author>John Smith</author>

<title>XML Retrieval</title>

<chapter> <heading>Introduction</heading>

This text explains all about XML and IR.

</chapter>

<chapter>

<heading> XML Query Language XQL

</heading>

<section>

<heading>Examples</heading>

</section>

<section>

<heading>Syntax</heading>

Now we describe the XQL syntax.

</section>

</chapter>

</book>

Example query

//chapter[about(.,

XML query language]

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Expressiveness


XML content typing: 2. Data Types

Data type: domain + (vague) predicates(see above)

Close relationship to XML Schema, but

XMLS supports syntactic type checking onlyNo support for vague predicates

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Expressiveness


XML content typing: 3. Object TypesBased on Tagging / Named Entity Recognition

Object types: Persons, Locations. Dates, .....

Pablo Picasso (October 25, 1881 - April 8, 1973) was aSpanish painter and sculptor..... In Paris, Picasso entertaineda distinguished coterie of friends in the Montmartre andMontparnasse quarters, including Andre Breton, GuillaumeApollinaire, and writer Gertrude Stein.

To which other artists did Picasso have close relationships?Did he ever visit the USA?

Named entity recognition methods allow for automaticmarkup of object types

Object types support increased precision

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Expressiveness


XML content typingTag semantics modelled as hierarchies

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Expressiveness


XML content typingTag semantics modelled in OWL

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Description Logic/Ontologies


ThesaurusIntroduction into OWLSPARQL



Thesaurus

regular

triangle

regular

polygon

polygon

rectangle

square

triangle quadrangle ...

thesaurus knowledge:can be expressed in propositional logicsquare = quadrangle ∧ regular-polygon

description logic

based on semantic networksmore expressive than thesauri

instances of conceptsroles between (instances of) concepts

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Thesaurus

regular

triangle

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Thesaurus

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Thesaurus

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Thesaurus

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Introduction into OWL

Semantic Web (ontology) languages

RDF: “Resource description language”semantic markup language, only resources and theirproperties, serialisation in XML

RDFS: “RDF Schema”, schema definition language for RDF

OWL: extends RDF/RDFS by richer modelling primitives,OWL Lite/DL/Full

OWL Lite contains simple primitivesOWL DL corresponds to expressive descriptionlogicOWL Full is OWL DL + RDF

knowledge base can be modelled as collection of RDFtriples (RDF/XML serialisation)alternative encoding: abstract syntax (easier to read)

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Objects, classes, literals and datatypes

Two distinct domains:

Classes: for objectsData types: for literals

Person

owl:Class owl:Datatype

Peter 1,89

rdf:type rdf:type

rdf:type rdf:type

xsd:decimal

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Classes (1)

owl:Class

ManMale

Animal Person

Femaleowl:disjointWith

rdfs:subClassOfrdfs:subClassOf

rdfs:subClassOf

rdfs:subClassOf

rdf:type

Class(Female partial Animal)

<owl:Class rdf:ID="Female">

<rdfs:subClassOf rdf:resource="#Animal"/>

</owl:Class>

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Classes (2)

owl:Class

ManMale

Animal Person

Femaleowl:disjointWith

rdfs:subClassOfrdfs:subClassOf

rdfs:subClassOf

rdfs:subClassOf

rdf:type

Class(Male partial Animal)

DisjointClasses(Male Female)

<owl:Class rdf:ID="Male">


<owl:disjointWith rdf:resource="#Female"/>

</owl:Class>

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Object properties (1)

owl:ObjectProperty

Animal Animalrdfs:domain

rdfs:rangehasFather Male

rdfs:rangehasParent

rdf:type

owl:subPropertyOf

ObjectProperty(hasParent domain(Animal) range(Animal))

<owl:ObjectProperty rdf:ID="hasParent">

<rdfs:domain rdf:resource="#Animal"/>

<rdfs:range rdf:resource="#Animal"/>

</owl:Class>

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Object properties (2)

owl:ObjectProperty

Animal Animalrdfs:domain

rdfs:rangehasFather Male

rdfs:rangehasParent

rdf:type

owl:subPropertyOf

ObjectProperty(hasFather super(hasParent) range(Male))

<owl:ObjectProperty rdf:ID="hasFather">

<rdfs:subPropertyOf rdf:resource="#hasParent"/>

<rdfs:range rdf:resource="#Male"/>

</owl:Class>

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Datatype properties

rdfs:domain rdfs:range

rdf:type

owl:DatatypeProperty

shoesizePerson xsd:decimal

rdf:type

owl:FunctionalProperty

DatatypeProperty(shoesize Functional domain(Animal) range(xsd:decimal))

<owl:DatatypeProperty rdf:ID="shoesize">

<rdfs:domain rdf:resource="#Animal"/>

<rdfs:range rdf:resource="xsd:decimal"/>

<rdf:type rdf:resource="owl:FunctionalProperty"/>

</owl:Class>

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Property restrictions

Class(Person partial Animal restriction(hasParent allValuesFrom(Person))

restriction(hasParent cardinality(2)))

<owl:Class rdf:ID="Person">


<rdfs:subClassOf>

<owl:Restriction>

<owl:onProperty rdf:resource="#hasParent"/>

<owl:allValuesFrom rdf:resource="#Person"/>

</owl:Restriction>

</rdfs:subClassOf>

<rdfs:subClassOf>

<owl:Restriction>

<owl:onProperty rdf:resource="#hasParent"/>

<owl:cardinality>2</owl:cardinality>

</owl:Restriction>

</rdfs:subClassOf>

</owl:Class>

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Instances

Individual(Kain type(Male) value(hasFather Adam)

value(hasMother Eve)

value(shoesize 10))

<Male rdf:ID="Kain">

<hasFather rdf:resource="#Adam"/>

<hasMother rdf:resource="#Eve"/>

<shoesize>10</shoesize>

</Male>

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Further modelling primitives

owl:inverseOf: inverse property: p(a, b)↔ r(b, a)

owl:TransitiveProperty: p(a, b), p(b, c)→ p(a, c)

owl:SymmetricProperty: p(a, b)→ p(b, a)

owl:InverseFunctionalProperty: inverse property is functional

owl:hasValue at least one property value equals object or datatypevalue

owl:someValuesFrom at least one property value is instance ofclass, expression or datatype

owl:interSectionOf, owl:unionOf, owl:complementOf: booleancombinations of class expressions

owl:oneOf: define class by enumerating its instances

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Limitations of OWL

OWL lacks support for

uncertainty: only deterministic relationships possible,no weighting or probabilistic facts⇒ “Pr(hasFather(lisa,thomas))=0.9” cannot be expressed

rules: no general rules,only specific rules like subClassOf, TransitiveProperty . . .⇒ “if hasParent(A,B) and hasParent(C,D) andhasSibling(B,D), then hasCousin(A,C)” cannot be expressed

n-ary datatype predicates:OWL datatypes are based on XML Schema datatypes, thusproviding only unary datatype predicates⇒ “sameDomain([email protected],[email protected])” cannot beexpressed

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Limitations of OWL









Limitations of OWL









Limitations of OWL









Limitations of OWL









OWL: Conclusion

OWL extends RDF(S) by additional modelling primitives

well-defined semantics, based on description logics

does not support all RDF features (no reification, only threelevels owl:Class, classes and objects)

lacks important features:

only deterministic features, no probabilistic relationshipsno rules (but in SWRL)restricted datatype predicates (due to XML Schema)

OWL and associated languages become standard in theSemantic Web

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Semantic Web Layers

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SPARQL

SPARQL

query language for getting information from RDF (OWL) graphsFacilities for

extract information in the form of URIs, blank nodes, plainand typed literals

extract RDF subgraphs

construct new RDF graphs based on information in thequeried graphs

Features:

matching graph patterns

variables – global scope; indicated by ’?’ or ‘$‘

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SPARQL

SPARQL: Basic Graph Pattern

Set of Triple Patterns

Triple Pattern – similar to an RDF Triple (subject, predicate,object), but any component can be a query variable; literalsubjects are allowed?book dc:title ?title

Matching a triple pattern to a graph: bindings betweenvariables and RDF Terms

Matching of Basic Graph Patterns

A Pattern Solution of Graph Pattern GP on graph G is anysubstitution S such that S(GP) is a subgraph of G.SELECT ?x ?v WHERE ?x ?v ?x

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SPARQL

SPARQL: Group Patterns + Value Constraints

Group Pattern: A set of graph patterns which must all matchValue Constraints: restrict RDF terms in a solutionSELECT ?n WHERE

?n profession "Physicist" . ?n isa "Politician"

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SPARQL

SPARQL: Query forms

SELECT returns all, or a subset of the variables bound in aquery pattern matchformats : XML or RDF/XML

CONSTRUCT returns an RDF graph constructed by substitutingvariables in a set of triple templates

DESCRIBE returns an RDF graph that describes the resourcesfound.

ASK returns whether a query pattern matches or not.

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Conclusion and Outlook




Conclusion

Inference

Probabilistic relational model supports integration of IR+DB

Probabilistic Datalog as powerful inference mechanism

Allows for formulating retrieval strategies as logical rules

Vague predicates

Natural extension of IR methods to attribute values

Vague predicates can be learned from feedback data

Transition from propositional to predicate logic

Expressive query language

Joins

Aggregations

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Conclusion

Inference




Vague predicates





Joins

Aggregations




Conclusion

Inference




Vague predicates





Joins

Aggregations


http://www.eecs.qmul.ac.uk/~thor/

http://www.spinque.com/



OutlookIR Systems vs. DBMS

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Separation between IRS and IR application?

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Towards an IRMS

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Towards an IRMS

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Towards an IRMS

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References

References I

Dalvi, N. N.; Suciu, D.(2007).Efficient query evaluation on probabilistic databases.VLDB J. 16(4), pages 523–544.

Forst, J. F.; Tombros, A.; Roelleke, T.(2007).POLIS: A Probabilistic Logic for Document Summarisation.In: Proceedings of the 1st International Conference on Theory of InformationRetrieval (ICTIR 07) - Studies in Theory of Information Retrieval, pages201–212.

Frommholz, I.; Fuhr, N.(2006).Probabilistic, Object-oriented Logics for Annotation-based Retrieval in DigitalLibraries.In: Nelson, M.; Marshall, C.; Marchionini, G. (eds.): Opening InformationHorizons – Proc. of the 6th ACM/IEEE Joint Conference on Digital Libraries(JCDL 2006), pages 55–64. ACM, New York.

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References

References II

Fuhr, N.; Lalmas, M.(2007).Advances in XML retrieval: the INEX initiative.In: IWRIDL ’06: Proceedings of the 2006 international workshop on Researchissues in digital libraries, pages 1–6. ACM, New York, NY, USA.

Fuhr, N.; Rolleke, T.(1997).A Probabilistic Relational Algebra for the Integration of Information Retrievaland Database Systems.ACM Transactions on Information Systems 14(1), pages 32–66.

Fuhr, N.; Rolleke, T.(1998).HySpirit – a Probabilistic Inference Engine for Hypermedia Retrieval in LargeDatabases.In: Proceedings of the 6th International Conference on Extending DatabaseTechnology (EDBT), pages 24–38. Springer, Heidelberg et al.

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References

References III

Fuhr, N.(1990).A Probabilistic Framework for Vague Queries and Imprecise Information inDatabases.In: Proceedings of the 16th International Conference on Very Large Databases,pages 696–707. Morgan Kaufman, Los Altos, California.

Fuhr, N.(2000).Probabilistic Datalog: Implementing Logical Information Retrieval for AdvancedApplications.Journal of the American Society for Information Science 51(2), pages 95–110.

Lalmas, M.; Roelleke, T.; Fuhr, N.(2002).Intelligent Hypermedia Retrieval.In: Szczepaniak, P. S.; Segovia, F.; Zadeh, L. A. (eds.): Intelligent Explorationof the Web, pages 324–344. Springer, Heidelberg et al.

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References

References IV

Pearl, J.(1988).Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference.Morgan Kaufman, San Mateo, California.

Rolleke, T.; Wu, H.; Wang, J.; Azzam, H.(2007).Modelling retrieval models in a probabilistic relational algebra with a newoperator: the relational Bayes.The International Journal on Very Large Data Bases (VLDB) 17(1), pages 5–37.

Suciu, D.; Olteanu, D.; Re, C.; Koch, C.(2011).Probabilistic Databases.Morgan & Claypool Publishers.

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