preference handling in relational query languages

Situation The Problem The Solution Contributions

Preference Handling in Relational QueryLanguages

Radim Nedbal

Czech Technical University in Prague,Fakulty of Nuclear Sciences and Physical Engineering

Prague, 7th October 2011

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Preference Handling in Relational QueryLanguages

Radim Nedbal

Czech Technical University in Prague,Fakulty of Nuclear Sciences and Physical Engineering

Prague, 7th October 2011

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Contents

1 SituationAutonomous systems should make desirable choicesDesirable choices can be intensionally denoted in a RQL

2 The ProblemDesirable feasible choices can’t be denoted in a RQLManual selection is opaque to the system

3 The SolutionA declarative language for preferences conditional on thecontext represented as a relational DB instanceSpecifying and interpreting preferencesRetrieving the most desirable choices

4 ContributionsSummary and conclusionsRelated work

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Contents

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Contents

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Contents

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Autonomous systems should make choices most desirable at the current context

Complex autonomous systems (CAS)

Environment

CAS Decision most desirable

actions

A framework for selecting the most d e s i r a b l ef e a s i b l e c h o i c e s at run-time

declarative specification of (designer’s) d e s i r e s,amenable to customization

by allowing specification of additional d e s i r e s,by providing additional information about the c o n t e x t.

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Environment

actions

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Environment

actions

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Environment

actions

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System configuration & design example

INPUT SCR. MAP ROOM

mC C...

CAMERA ROOM IR LIT GATE

A1 A N 0.2 0A2 A N 0.2 0A3 A N 1 1A4 A N 1 1A5 A Y 0.3 0.04

MAP mA

A1 A2A3 A4

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INPUT SCR.mA s1

MAP ROOM

mC C...

MAP mA

A1 A2A3 A4

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INPUT SCR.mA s1A3 s2A4 s2

MAP ROOM

mC C...

MAP mA

A1 A2A3 A4

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INPUT SCR.mA s1A3 s2A4 s2A5 s2

MAP ROOM

mC C...

MAP mA

A1 A2A3 A4

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INPUT SCR. MAP ROOM

mC C...

A1 A N 0 0A2 A N 0 0A3 A N 0 1A4 A N 0 1A5 A Y 0 0.04

MAP mA

A1 A2A3 A4

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INPUT SCR.A5 s1A3 s2

MAP ROOM

mC C...

MAP mA

A1 A2A3 A4

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INPUT SCR. MAP ROOM

mC C...

MAP mA

A1 A2A3 A4

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INPUT SCR.mA s1

MAP ROOM

mC C...

MAP mA

A1 A2A3 A4

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INPUT SCR.mA s1A3 s2A4 s2

MAP ROOM

mC C...

MAP mA

A1 A2A3 A4

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INPUT SCR.mA s1A3 s2A4 s2A1 s2A2 s2

MAP ROOM

mC C...

MAP mA

A1 A2A3 A4

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Desirable choices can be intensionally denoted by their properties in a RQL

DB of feasible choices

INPUT SCR.mA s1

......

MAP ROOM

mA AmB B

mC C...

CAMERA ROOM IR LIT GATE...

......

A4 A N 1 1A5 A Y 0.3 0.04B1 B N 0 1...

......

Maps of rooms where some non-IR cameras shoot a lit areaR(xmap, s1)←− S(xmap, xroom) ∧ T (xcamera, xroom, “N”,1, xgate)

R( mA, s1)←− S( mA , A ) ∧ T ( A4 , A , “N”,1, 1 )

A DB query1 is system interpretable specification of desirable choices,2 can be re-evaluated when DB changes.

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DB of feasible choices

INPUT SCR.mA s1

......

MAP ROOM

mA AmB B

mC C...

CAMERA ROOM IR LIT GATE...

......

A4 A N 1 1A5 A Y 0.3 0.04B1 B N 0 1...

......

Maps of rooms where some non-IR cameras shoot a lit areaR(xmap, s1)←− S(xmap, xroom) ∧ T (xcamera, xroom, “N”,1, xgate)

R( mA, s1)←− S( mA , A ) ∧ T ( A4 , A , “N”,1, 1 )

A DB query1 is system interpretable specification of desirable choices,2 can be re-evaluated when DB changes.

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A DB query specifies desirable characteristics

Non-IR cameras shooting a lit gate area.

ans(xcamera)←− T (xcamera, xroom, xIR, xlit, xgate) ∧xIR = “N” ∧ xlit = 1 ∧ xgate = 1 .

T : relation of installed cameras,x IR = “N” : non-IR cameras,

x lit = 1 : cameras shooting a lit area,xgate = 1 : cameras shooting a gate area.

(Most) desirable feasible choices are what matters (most)!

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(Most) desirable feasible choices can’t be intensionally denoted by their properties in a RQL

Little knowledge to specify characteristics of feasible choices

Asking too specifically 99K empty result effect.(Satisfiability of DB queries is undecidable)

+ Adjust characteristics or give up!Asking for too little 99K flooding effect.

+ Manual selection!

Gradual adjusting original characteristics

+ Add or remove characteristics!

+ Relax or tighten up characteristics!

b expensive as space of characteristics is combinatorially huge!b infeasible in the case of automated decision making

(autonomous agents)!!7,/,30

+ Manual selection!

Gradual adjusting characteristics

x IR = “N” : non-IR cameras,x lit = 1 : cameras shooting a lit area,

xgate = 1 : cameras shooting a gate area.

x IR = “N” ∧ x lit = 1 ∧ xgate = 1

x IR = “N” ∧ x lit = 1x IR = “N” ∧ xgate = 1

x lit = 1 ∧ xgate = 1

x IR = “N” x lit = 1 xgate = 1

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x IR = “N” ∧ x lit = 1 ∧ xgate = 1

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x IR = “N” ∧ x lit = 1 ∧ xgate = 1

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x IR = “N” ∧ x lit = 1 ∧ xgate = 1

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x IR = “N” ∧ x lit = 1 ∧ xgate = 1

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x IR = “N” ∧ x lit = 1 ∧ xgate = 1

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x IR = “N” ∧ x lit = 1 ∧ xgate = 1

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x IR = “N” ∧ x lit = 1 ∧ xgate = 1

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Manual selection or adjusting characteristics of desired choices is opaque to the system

Reasons behind manual selection of adjustingare opaque to the system,are someone’s “liking of one thing more than another,” i.e.,various desirability of respective answers,are what we term preferences.

Preferences are wishes!No perfect match?? 99K worse alternatives.A paradigm shift

from exact matches towards a best possible match-making,from h a r d c o n s t r a i n t s to s o f t c o n s t r a i n t s.

The main goal of the thesisa general framework for incorporating preferences in RQLto support the user-friendly design of autonomous systems thatcan act in dynamic environment.

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Reasons behind manual selection of adjustingare opaque to the system,are someone’s “liking of one thing more than another,”i.e., various desirability of respective answers,are what we term preferences.

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Reasons behind manual selection of adjustingare opaque to the system,are someone’s “liking of one thing more than another,”i.e., various desirability of respective answers,are what we term preferences.

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Requirements

q(J)Preferences

Manual designation

q∗(J)

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Requirements

q(J)Preferences

Manual designation

q∗(J)

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Requirements

PreferencesP

Manual designation

q∗(J)

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Requirements

q(J)Preferences

Manual designation

q∗(J)

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Requirements

q(J)Preferences

Manual designation

Requirements,preferences

q∗(J)

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Requirements

q(J)Preferences

Manual designation

q∗(J)

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Requirements

q(J)Preferences

Manual designation

q∗(J)

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Back to MM

Back to Representationþ

Requirements

q(J)Preferences

Manual designation

q∗(J)

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A declarative language for preferences conditional on the current state of the world represented as a relational DB instance

Concretization of the basic concepts To J, q,P

Models Language Algorithms

Interpretation Representation

Data model

RDM The most desirable choices

A nonempty setof distinguished

preference models

Partial pre-orders Heterogenous andpossibly conflicting

preference formulae of LP

Non-monotonic reasoningSubmodels of distinguished

preference models

DDP and DBS

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Data model

preference models

DDP and DBS

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Data model

preference models

DDP and DBS

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Data model

preference models

DDP and DBS

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Data model

preference models

DDP and DBS

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Data model

preference models

DDP and DBS

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Data model

preference models

DDP and DBS

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Data model

preference models

Heterogenous andpossibly conflicting

preference models

DDP and DBS

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Data model

preference models

DDP and DBS

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Data model

preference models

DDP and DBS

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Data model

preference models

DDP and DBS

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Data model

preference models

DDP and DBS

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Specifying and interpreting preferences

Models Back to the meta-model

are structures that capture properties of specified preferences

Preference model 〈Ω,〉is a partial pre-orderover a set Ω of a c c e p t a b l e f e a s i b l e choice.

reflexive, transitive, partial.

WALKING

SUBWAY

WALKING

TAXI WALKING

SUBWAY

TAXI WALKING

SUBWAY

b Ω is abstracted as q(J);b w w ′ (w w ′) reads: “w is (strictly) preferred to w ′.”

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WALKING

SUBWAY

WALKING

TAXI WALKING

SUBWAY

TAXI WALKING

SUBWAY

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WALKING

SUBWAY

WALKING

TAXI WALKING

SUBWAY

TAXI WALKING

SUBWAY

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WALKING

SUBWAY

WALKING

TAXI WALKING

SUBWAY

TAXI WALKING

SUBWAY

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WALKING

SUBWAY

WALKING

TAXI WALKING

SUBWAY

TAXI WALKING

SUBWAY

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WALKING

SUBWAY

WALKING

TAXI WALKING

SUBWAY

TAXI WALKING

SUBWAY

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Language Back to the meta-model

encodes preferences by specifying models

Language of preference formulae LP

ϕB ψ is a preference formula (of LP) iffϕ,ψ are DB queries “of the same type,”B is represents a recognized kind of a preference.

ϕ1m>M ψ ,

ϕ2M>M ψ ,

ϕ3m>m ψ ,

ϕ4M>m ψ ,

q(J)ψ(J)

ϕ1(J)

ϕ2(J)

ϕ3(J)

ϕ4(J)

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ϕ1m>M ψ ,

ϕ2M>M ψ ,

ϕ3m>m ψ ,

ϕ4M>m ψ ,

ϕ1(J)

ϕ2(J)

ϕ3(J)

ϕ4(J)

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ϕ1m>M ψ ,

ϕ2M>M ψ ,

ϕ3m>m ψ ,

ϕ4M>m ψ ,

q(J)ψ(J)

ϕ1(J)

ϕ2(J)

ϕ3(J)

ϕ4(J)

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ϕ1m>M ψ ,

ϕ2M>M ψ ,

ϕ3m>m ψ ,

ϕ4M>m ψ ,

q(J)ψ(J)

ϕ1(J)

ϕ2(J)

ϕ3(J)

ϕ4(J)

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ϕ1m>M ψ ,

ϕ2M>M ψ ,

ϕ3m>m ψ ,

ϕ4M>m ψ ,

q(J)ψ(J)

ϕ1(J)

ϕ2(J)

ϕ3(J)

ϕ4(J)

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ϕ1m>M ψ ,

ϕ2M>M ψ ,

ϕ3m>m ψ ,

ϕ4M>m ψ ,

q(J)ψ(J)

ϕ1(J)

ϕ2(J)

ϕ3(J)

ϕ4(J)

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ϕ1m>M ψ ,

ϕ2M>M ψ ,

ϕ3m>m ψ ,

ϕ4M>m ψ ,

q(J)ψ(J)

ϕ1(J)

ϕ2(J)

ϕ3(J)

ϕ4(J)

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Interpretation Back to the meta-model

gives exact meaning to preference formulae

P = ϕ m>M ψ ,ψ m>M ω ϕ ∧ ψ ∧ ¬ω ? ϕ ∧ ¬ψ

1 Minimal logic of preference:+ w is as good as w ′ iff allowed by P

+ each P is satisfied by one or more models!2 Non-monotonic reasoning mechanism: yields DPMs.

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P = ϕ m>M ψ ,ψ m>M ω ϕ ∧ ψ ∧ ¬ω ? ϕ ∧ ¬ψ

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P = ϕ m>M ψ ,ψ m>M ω ϕ ∧ ψ ∧ ¬ω ? ϕ ∧ ¬ψ

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P = ϕ m>M ψ ,ψ m>M ω ϕ ∧ ψ ∧ ¬ω ? ϕ ∧ ¬ψ

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P = ϕ m>M ψ ,ψ m>M ω ϕ ∧ ψ ∧ ¬ω ? ¬ϕ ∧ ψ ∧ ω

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P = ϕ m>M ψ ,ψ m>M ω ϕ ∧ ψ ∧ ¬ω ? ¬ϕ ∧ ψ ∧ ω

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P = ϕ m>M ψ ,ψ m>M ω ϕ ∧ ψ ∧ ¬ω ? ϕ ∧ ¬ψ

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P = ϕ m>M ψ ,ψ m>M ω ϕ ∧ ψ ∧ ¬ω ? ϕ ∧ ¬ψ

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P = ϕ m>M ψ ,ψ m>M ω ϕ ∧ ψ ∧ ¬ω ? ϕ ∧ ¬ψ

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Retrieving the most desirable choices

Representation Back to the meta-model

captures preference formulae in a framework suitable for algorithms

q′(J)

Due to Theorem 3, we can find q′(J),

q′(J) ⊆ q(J) ,

so thatthe set of DPMs with underlying set q′(J)determinesthe set of DPMs with underlying set q(J)

Any P can be represented compactly: To J, q,P

the set ofd i s t i n g u i s h e d p r e f e r e n c e m o d e l s,

+ defining the meaning of P

can be represented asthe set of t h e i r s u b m o d e l s.

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q′(J)ψ(J)

q′(J) ⊆ q(J) ,

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q′(J)

q′(J) ⊆ q(J) ,

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q′(J)ψ(J)

q′(J) ⊆ q(J) ,

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q′(J)ψ(J)

q′(J) ⊆ q(J) ,

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q′(J)

q′(J) ⊆ q(J) ,

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q′(J)

q′(J) ⊆ q(J) ,

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Algorithms To Algorithm 2 Back to the meta-model

MDC w.r.t. J, q, P = ϕ m>M ψ ,ψ m>M ω

q′(J)

q(J)ϕ m>M ψ : g b ∧ e b

ψ m>M ω : d a ∧ d g

transitivity:

x z ∧ y ∈ a, . . . ,g → x y ∨ y z

J,q,P DPMsDecl. sem.Theorems 1,2

// DPMs MDC//

Repres.

Theorem 3

Alg.1, Theo.4//

Constr. sem.

R-MDC//

Theorem 5

[q∧ϕ∧ψ∧¬ω](J)

[q∧ϕ∧¬ψ∧¬ω](J)

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q′(J)

transitivity:

x z ∧ y ∈ a, . . . ,g → x y ∨ y z

// DPMs MDC//

Repres.

Theorem 3

Alg.1, Theo.4//

Constr. sem.

R-MDC//

Theorem 5

[q∧ϕ∧ψ∧¬ω](J)

[q∧ϕ∧¬ψ∧¬ω](J)

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q′(J)

transitivity:

x z ∧ y ∈ a, . . . ,g → x y ∨ y z

// DPMs MDC//

Repres.

Theorem 3

Alg.1, Theo.4//

Constr. sem.

R-MDC//

Theorem 5

[q∧ϕ∧ψ∧¬ω](J)

[q∧ϕ∧¬ψ∧¬ω](J)

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q′(J)

ϕ m>M ψ : g b ∧ e b

transitivity:

x z ∧ y ∈ a, . . . ,g → x y ∨ y z

// DPMs MDC//

Repres.

Theorem 3

Alg.1, Theo.4//

Constr. sem.

R-MDC//

Theorem 5

[q∧ϕ∧ψ∧¬ω](J)

[q∧ϕ∧¬ψ∧¬ω](J)

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q′(J)

transitivity:

x z ∧ y ∈ a, . . . ,g → x y ∨ y z

// DPMs MDC//

Repres.

Theorem 3

Alg.1, Theo.4//

Constr. sem.

R-MDC//

Theorem 5

[q∧ϕ∧ψ∧¬ω](J)

[q∧ϕ∧¬ψ∧¬ω](J)

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q′(J)

transitivity:

x z ∧ y ∈ a, . . . ,g → x y ∨ y z

// DPMs MDC//

Repres.

Theorem 3

Alg.1, Theo.4//

Constr. sem.

R-MDC//

Theorem 5

[q∧ϕ∧ψ∧¬ω](J)

[q∧ϕ∧¬ψ∧¬ω](J)

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q′(J)

transitivity:

x z ∧ y ∈ a, . . . ,g → x y ∨ y z

// DPMs MDC//

Repres.

Theorem 3

Alg.1, Theo.4//

Constr. sem.

R-MDC//

Theorem 5

[q∧ϕ∧ψ∧¬ω](J)

[q∧ϕ∧¬ψ∧¬ω](J)

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q′(J)

transitivity:

x z ∧ y ∈ a, . . . ,g → x y ∨ y z

// DPMs MDC//

Repres.

Theorem 3

Alg.1, Theo.4//

Constr. sem.

R-MDC//

Theorem 5

[q∧ϕ∧ψ∧¬ω](J)

[q∧ϕ∧¬ψ∧¬ω](J)

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Summary and conclusions

The proposed frameworkis general enough to have wide applicability

A novel, flexible approach based on the language capableof encoding qualitative comparative preference statements

1 that may be of various kinds2 that may be nondeterministic;3 that may be context sensitive4 that may be augmented by mandatory requirements.

is suitable for control of dynamic systems, where both thestate and number of objects changes.

A camera stream of a gate area is always desirable.+ .. an arbitrary such a camera.

Streams from non-IR cameras shooting a lit area are moredesirable than streams from IR cameras.+ .. currently lit areas wrt. the updated DB.

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The proposed frameworkis formal enough to support automated decision making

1 Preferences are embedded in RQLs.2 The empty result effect is eliminated:

+ any preference specification has a DPMTheorem 1(totality of interpretation).

3 Constructive semantics is based on a compactrepresentation (Theorem 3).

from which DPMs can be inferred;which can be encoded as a DDP.

+ We exploit DDP machinery (Algorithm 1, Theorem 4)to compute DPMs.

4 MDC are denoted as a DB query (Theorem 5)and retrieved from the DB, exploiting standard DBoptimization strategies.

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Related work

Influential paper, projects, and figures

M. Lacroix and Pierre Lavency.Preferences: Putting More Knowledge into Queries.VLDB, 1987.

1999 –(8 projects)

It’s a Preference WorldUniversity of Augsburg

Germany

WernerKießling

2003 –Preference QueriesUniversity at Buffalo

JanChomicki

? –Command & ControlBen-Gurion University

Beer-Sheva, Israel

Ronen I.Brafman

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Related work

Comparison to related work

Preference model Language Interpretation

Granularity

Context

Lacroix and Lavency 1987 X X X X XKießling 2002 X X X XChomicki 2002; 2003 X X (X) X X XHolland and Kießling 2004 X X X XBrafman and Domshlak 2004 X X X X XAgrawal et al. 2006 X X X XEndres and Kießling 2006 X X X X XCiaccia 2007 X X X XMindolin and Chomicki 2007 X X X X XGeorgiadis et al. 2008 X X X X XKaci and Neves 2010 X X X X X XZhang and Chomicki 2011 X X X XThe presented approach X X X X X X X X

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Appendix

INPUT SCR.mA s1A3 s2

MAP ROOM

mC C...

MAP mA

A1 A2A3 A4

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Appendix

MAP ROOM

mC C...

MAP mA

A1 A2A3 A4

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Appendix

MAP ROOM

mC C...

MAP mA

A1 A2A3 A4

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Appendix

MAP ROOM

mC C...

MAP mA

A1 A2A3 A4

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Appendix

MAP ROOM

mC C...

MAP mA

A1 A2A3 A4

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Appendix

MAP ROOM

mC C...

MAP mA

A1 A2A3 A4

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Appendix

ϕ1m>M ψ ,

ϕ2M>M ψ ,

ϕ3m>m ψ ,

ϕ4M>m ψ ,

q(J)ψ(J)

ϕ1(J)

ϕ2(J)

ϕ3(J)

ϕ4(J)

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Appendix

ϕ1m>M ψ ,

ϕ2M>M ψ ,

ϕ3m>m ψ ,

ϕ4M>m ψ ,

q(J)ψ(J)

ϕ1(J)

ϕ2(J)

ϕ3(J)

ϕ4(J)

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Appendix

ϕ1m>M ψ ,

ϕ2M>M ψ ,

ϕ3m>m ψ ,

ϕ4M>m ψ ,

q(J)ψ(J)

ϕ1(J)

ϕ2(J)

ϕ3(J)

ϕ4(J)

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Appendix

ϕ1m>M ψ ,

ϕ2M>M ψ ,

ϕ3m>m ψ ,

ϕ4M>m ψ ,

q(J)ψ(J)

ϕ1(J)

ϕ2(J)

ϕ3(J)

ϕ4(J)

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Appendix

ϕ1m>M ψ ,

ϕ2M>M ψ ,

ϕ3m>m ψ ,

ϕ4M>m ψ ,

q(J)ψ(J)

ϕ1(J)

ϕ2(J)

ϕ3(J)

ϕ4(J)

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Appendix

ϕ1m>M ψ ,

ϕ2M>M ψ ,

ϕ3m>m ψ ,

ϕ4M>m ψ ,

q(J)ψ(J)

ϕ1(J)

ϕ2(J)

ϕ3(J)

ϕ4(J)

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Appendix

gives exact meaning to preference formulaeP = ϕ m>M ψ ,ψ m>M ω ϕ ∧ ψ ∧ ¬ω ? ϕ ∧ ¬ψ

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Appendix

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Appendix

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Appendix

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Appendix

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Appendix

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Appendix

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Appendix

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Appendix

q′(J)ψ(J)

q′(J) ⊆ q(J) ,

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Appendix

q′(J)

transitivity:

x z ∧ y ∈ a, . . . ,g → x y ∨ y z

// DPMs MDC//

Repres.

Theorem 3

Alg.1, Theo.4//

Constr. sem.

R-MDC//

Theorem 5

[q∧ϕ∧ψ∧¬ω](J)

[q∧ϕ∧¬ψ∧¬ω](J)

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Appendix

q′(J)

transitivity:

x z ∧ y ∈ a, . . . ,g → x y ∨ y z

// DPMs MDC//

Repres.

Theorem 3

Alg.1, Theo.4//

Constr. sem.

R-MDC//

Theorem 5

[q∧ϕ∧ψ∧¬ω](J)

[q∧ϕ∧¬ψ∧¬ω](J)

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Appendix

q′(J)

transitivity:

x z ∧ y ∈ a, . . . ,g → x y ∨ y z

// DPMs MDC//

Repres.

Theorem 3

Alg.1, Theo.4//

Constr. sem.

R-MDC//

Theorem 5

[q∧ϕ∧ψ∧¬ω](J)

[q∧ϕ∧¬ψ∧¬ω](J)

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Appendix

q′(J)

transitivity:

x z ∧ y ∈ a, . . . ,g → x y ∨ y z

// DPMs MDC//

Repres.

Theorem 3

Alg.1, Theo.4//

Constr. sem.

R-MDC//

Theorem 5

[q∧ϕ∧ψ∧¬ω](J)

[q∧ϕ∧¬ψ∧¬ω](J)

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Appendix

Algorithm 2 for computation of most preferred matches To algorithms

Require: P,q,J.Ensure: The most preferred tuples wrt. P that fulfill q.

1: Construct UP . . Step I. (see page 68)2: Construct rules of P. . Step II. (see page 72)3: Add rules ensuring transitivity. . Step III. (see page 74)4: Compute O. . Algorithm 1 on page 775: Determine O<.6: Compute SMJ

7: Compute MX(SMJ

.8: Translate q together with elements from MX

into a RQL formula q′.9: Evaluate q′(J) – the most preferred matches. . DBMS

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Appendix

P,Ω,J IP(Ω,J)declarativesemantics

//_______ IP(Ω,J) = UEΩP

(⋃αΩ αΩ= UEΩ

(⋃αΩ αΩ

)))IP(Ω,J)

MX (IP (Ω,J)) =

MX (IP (Ω,J)) =⋃

wk∈MX(IP(UP ,J)

)Dom(wk )

P,Ω,J

OOOOOOOOOOO

?OOOOOOOOOOO

P O<4,5

constructivesemantics

// O< EMJP

(MODP(UP ,J)

))IP (UP ,J)IP (UP ,J)

IP (UP ,J)

MX (IP (UP ,J))

YYMX (IP (UP ,J))

⋃wk∈MX

(IP(UP ,J)

)Dom(wk )

29,/,30

Appendix

Germany

Werner

Kießling

Chomicki

Beer-Sheva, Israel

Ronen I.

Brafman30,/,30

Appendix

Germany

Werner

Kießling

Chomicki

Beer-Sheva, Israel

Ronen I.

Brafman

30,/,30

Appendix

Germany

Werner

Kießling

Chomicki

Beer-Sheva, Israel

Ronen I.

Brafman

30,/,30

Appendix

Germany

Werner

Kießling

Chomicki

Beer-Sheva, Israel

Ronen I.

Brafman30,/,30

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