Qualitative Preferences Tools and Applications Ganesh Ram Santhanam 1 Samik Basu 1 amp Vasant Honavar 2 1 Iowa State University 2 Penn State University gsanthaniastateedu ID: 618903
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Slide1
Representing & Reasoning with Qualitative Preferences: Tools and Applications
Ganesh Ram Santhanam1, Samik Basu1 & Vasant Honavar21Iowa State University, 2 Penn State Universitygsanthan@iastate.edu
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.Slide2
Outline
Qualitative Preference LanguagesRepresentation : Syntax of languages CP-nets, TCP-nets, CI-nets, CP-TheoriesQualitative Preference LanguagesCeteris Paribus semantics: the induced preference graph (IPG)Reasoning: Consistency, Dominance, Ordering, Equivalence & SubsumptionComplexity of ReasoningPractical aspects: Preference Reasoning via Model CheckingFrom ceteris paribus semantics (IPG) to Kripke structures Specifying and verifying properties in temporal logicTranslating Reasoning Tasks into Temporal Logic PropertiesRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
2Slide3
Outline
ApplicationsEngineering: Civil, Software (SBSE, RE, Services), Aerospace, ManufacturingSecurity: Credential disclosure, Cyber-securityAlgorithms: Search, Stable Marriage, Allocation, Planning, Recommender systemsEnvironmental applications: Risk Assessment, Policy decisions, Environmental impact, Computational SustainabilityiPref-R ToolA tool that does well in practice for a known hard problemArchitectureDemoUse of iPref-R in Security, Software EngineeringRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.3Slide4
Broad view of Decision TheoryWhat is a
decision? Choosing from a set of alternatives A Choice function: How are alternatives described? What influences choice of an agent? - preferences, uncertainty, risk Can decisions be automated? What happens if there are multiple agents? - conflicting preferences and choices“I prefer walking over driving to work”
There is a 50% chance of snow. Walking may not be good after all.
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
4Slide5
Qualitative Preferences
WalkingDrivingBusCarpooling
Qualitative
Quantitative
?
Walking = 0.7; Driving = 0.3
Walking = 0.6; Driving = 0.4
Walking
Driving
5
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
False sense of precision
False sense of completenessSlide6
Representation: Alternatives are Multi-attributed
Course selection - which course to take?Subject?Instructor? # Credits?Preference variables or attributes used to describe the domainAlternatives are assignments to preference variablesα = (instructor = Gopal, area = AI, credits = 3)α ≻ β denotes that α is preferred
to β
509
Gopal
Tom
Bob
AI
SE
NW
572
586
4
3
3
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
6Slide7
Qualitative Preference Languages
Qualitative preferencesUnconditional PreferencesTUP-nets [Santhanam et al., 2010]Conditional PreferencesCP-nets [Boutilier et al. 1997,2002]Models dependenciesRelative ImportanceTCP-nets [Brafman et al. 2006]CI-nets [Bouveret et al. 2009]Idea is to represent relative preferencesAI ≻area SE
SE : Tom
≻
instructor
Gopal
AI :
Gopal
≻
instructor
Tom
Instructor
⊳
Credits
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
7Slide8
Conditional Preference nets (CP-nets) [Boutilier et al., 1997]
CP-netsNodes – Preference VariablesEdges – Preferential Dependency between variablesConditional Preference Table (CPT) annotates nodesCPT can be partially specifiedRelative preferences over:Pairs of values of an attributeAreaInstructor
Credits
Intra-variable
preference
AI
≻
area
SE
AI:
Gopal
≻
instr
Tom
SE: Tom
≻
instr
Gopal
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
8
F
E
A
E=Functional:
Unavailable
≻
Official fix
LO
≻
HI
Functional
≻
UnprovenSlide9
Trade-off enhanced CP-nets (TCP-nets) [Brafman et al., 2006]
TCP-netsNodes – Preference VariablesEdges – Preferential Dependency between variables & Relative Importance over pairs of variablesConditional Preference Table (CPT) annotates nodesCPT can be partially specifiedComparative preferences over:Pairs of values of an attributePairs of attributes (importance)AreaInstructor
Credits
Relative Importance
Intra-variable
preference
AI
≻
area
SE
AI:
Gopal
≻
instr
Tom
SE: Tom
≻
instr
Gopal
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
9
F
E
A
E=Functional:
Unavailable
≻
Official fix
LO
≻
HI
Functional
≻
UnprovenSlide10
Conditional Preference Theories (CP-theories) [Wilson 2004,2006]
CP-TheoriesSimilar to TCP-nets but..Possible to express relative Importance of a variable over a set of variablesAreaInstructorCredits
Relative Importance
Intra-variable
preference
AI
≻
area
SE
AI:
Gopal
≻
instr
Tom
SE: Tom
≻
instr
Gopal
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
10
F
E
A
E=Functional:
Unavailable
≻
Official fix
LO
≻
HI
Functional
≻
UnprovenSlide11
Conditional Importance Networks (CI-nets) [Bouveret 2009]
CI-nets (fair division of goods among agents)Preference variables represent items to be included in a deal Preference variables are Binary (presence/absence of an item)Intra-variable Preference is monotonic (0 ≻ 1 or 1 ≻ 0)Subsets preferred to supersets (or vice versa) by defaultCI-net Statements are of the form S+, S− : S1 ≻ S2 Represents preference on the presence of one set of items over another set under certain conditions
If all propositions in S+ are true and all propositions in S- are false, then the set of propositions S
1
is preferred to
S
2
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
11Slide12
Conditional Importance Networks (CI-nets) [Bouveret 2009]
CI-nets (fair division of goods among agents)Example:Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.12
If I have to …
disclose
my
address
without
having to disclose
my
name
,
then
I
would prefer
…
giving my
bank routing number
over
…
my
bank account numberSlide13
Other Preference Languages
Preference languages in Databases [Chomicki 2004]Preferences over Sets [Brafman et al. 2006]Preferences among sets (incremental improvement)[Brewka et al. 2010]Tradeoff-enhanced Unconditional Preferences (TUP-nets) [Santhanam et al. 2010]Cardinality-constrained CI-nets (C3I-nets) [Santhanam et al. 2013]Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.13Slide14
Relative Expressivity of Preference LanguagesRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
14CI-netsCP-netsTCP-netsCP-theoriesTUP-netsC3I-nets
Preferences over
Multi-domain
Variables
Preferences over
(Sets
of) Binary Variables Slide15
Preference Reasoning
Focus of this tutorial :Exact Reasoning about Qualitative PreferencesNot covered : Uncertainty + PreferencesCornelio et al. Updates and Uncertainty in CP-Nets 2013Bigot et al. Probabilistic CP-nets 2013Applications Rossi et al. Preference Aggregation: Social Choice 2012Chomicki et al. Skyline queries in Databases 2011Trabelsi et al
. Preference Induction Recommender systems 2013Other Reasoning Approaches
Minyi
et al.
Heuristic
approach to dominance testing in CP-nets
2011
Nic
Wilson
Upper
Approximation for Conditional
Preferences
2006
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
15Slide16
Other Preference Languages
Preference languages in Databases [Chomicki 2004]Preferences over Sets [Brafman et al. 2006]Preferences among sets (incremental improvement)[Brewka et al. 2010]Tradeoff-enhanced Unconditional Preferences (TUP-nets) [Santhanam et al. 2010]Cardinality-constrained CI-nets (C3I-nets) [Santhanam et al. 2013]In this tutorial … We stick to CP-nets, TCP-nets and CI-netsApproach extensible to all other ceteris paribus preference languagesRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.16Slide17
Part II – Theoretical AspectsPart II
Theoretical Aspects of Representing & Reasoning with Ceteris Paribus PreferencesRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.17Slide18
Theoretical AspectsPart II – OutlineInduced Preference Graph (IPG)
Semantics in terms of flips in the IPGReasoning TasksDominance over AlternativesEquivalence & Subsumption of PreferencesOrdering of AlternativesComplexity of ReasoningRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.18Slide19
010
011
000
001
101
111
100
110
I
nduced
preference graph
δ
(P)=
G
(
V,E
) of preference spec P:
Nodes
V
: set of
alternatives
Edges
E
: (
α
,
β
) ∈
E
iff
there is a
flip induced by some statement in P
from
α
to
β
δ
(N) is acyclic (dominance is a strict partial order)
α
≻
β
iff
there is a
path
in
δ
(N) from
α
to
β
(serves as the
proof
)
Induced Preference Graph (IPG)
[
Boutilier
et al. 2001]
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
19
Santhanam et al. AAAI 2010Slide20
Preference Semantics in terms of IPG(α ,
β) ∈ E iff there is a flip from α to β “induced by some preference” in PTypes of flipsCeteris Paribus flip – flip a variable, “all other variables equal”Specialized flipsRelative Importance flipSet based Importance flipCardinality based Importance flipLanguages differ in the semantics depending on the specific types of flips they allow … Next: examplesRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.20Slide21
(α , β) ∈ E iff
there is a statement in CP-net such that x1 ≻1 x’1 (x1 is preferred to x’1) and …V-flip : all other variables being equal, α(X1)=x1 and β(X1)=x’1
Single
variable flip
– change value of 1 variable at a time
010
011
000
001
101
111
100
110
Flips for a CP-net
[
Boutilier
et al. 2001]
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
21
Ceteris paribus
(all else being equal)
V-flipSlide22
(α , β) ∈ E iff
there is a statement in TCP-net such that x1 ≻1 x’1 (x1 is preferred to x’1) and …V-flip : all other variables being equal, α(X1)=x1 and β(X1)=x’1I-flip : all variables except those less important than X1
being equal, α(X1)=x1
and
β
(X
1
)=x’
1
Multi
-variable
flip
– change values of multiple variables at a time
010
011
000
001
101
111
100
110
Flips for TCP-nets & CP-theories
[
Brafman
et al., Wilson 2004]
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
22
Relative
Importance
V
-flip
I
-flipSlide23
Flips for a CI-net [Bouveret 2009]
Recall: CI-nets express preferences over subsets of binary variables X. Truth values of Xi tells its presence/absence in a setNodes in IPG correspond to subsets of XSupersets are always preferred to Strict Subsets (convention)S+, S− : S1 ≻ S2 interpreted as … If all propositions in S+ are true and all propositions in S- are false, then the set of propositions S1 is preferred to S2For α , β ⊆
X, (α, β) ∈ E (β
preferred to
α
)
iff
M-flip
: all other variables being equal,
α
⊂
β
CI-flip
:
there is a CI-net
statement
s.t.
S
+
,
S
−
: S
1
≻
S
2 and α
, β satisfy S+, S− and α satisfies S
+ and β satisfies S-.
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.23Slide24
Flips for a CI-net [Bouveret 2009]
For α , β ⊆ X, (α, β) ∈ E (β preferred to α) iffM-flip : all other variables being equal, α ⊂ βCI-flip : there is a CI-net statement S+, S− : S1 ≻ S2 s.t.
α , β
satisfy
S
+
,
S
−
and
α
satisfies S
+
and
β
satisfies S
-
.
Example:
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
24
Oster et al. FACS 2012
M-flip
CI-flipSlide25
Flips for a C3I-net [Santhanam et al. 2013]
C3I-nets express preference over subsets similar to CI-net Truth values of Xi tells its presence/absence in a setNodes in IPG correspond to subsets of XSets with higher cardinality are preferred (conventional)S+, S− : S1 ≻ S2 interpreted as … If all propositions in
S+ are true and all propositions in S
-
are false, then
the set of propositions
S
1
is preferred to
S
2
For
α
,
β
⊆
X, (
α
,
β
) ∈
E
(
β
preferred to
α
)
iff
M-flip : all other variables being equal, |α| < |β|CI-flip
: there is a CI-net statement s.t. S
+, S− : S
1 ≻
S2 and
α ,
β
satisfy
S
+
,
S
−
and
α
satisfies S
+
and
β
satisfies S
-
.
Extra cardinality constraint to enable dominance
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
25Slide26
Flips for a C3I-net [Santhanam et al.
2013]For α , β ⊆ X, (α, β) ∈ E (β preferred to α) iffM-flip : α ⊂ β (all other variables being equal)CI-flip : there is a CI-net statement S+, S− : S1
≻ S2 s.t. α
,
β
satisfy
S
+
,
S
−
and
α
satisfies S
+
and
β
satisfies S
-
.
C-flip
: |
α
| < |
β
|
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
26
Santhanam
et al. CSIIRW 2013
C-flip - present in the CI-net, but
not
in the C
3
I-net
{c}
≻
{
bc
} due to
Monotonicity
{
bc
}
≻
{
bd
} due to
P2
{
ab
}
⊁
{c} due to
Cardinality
despite
P3
M-flip
CI
-flipSlide27
Reasoning Tasks
Now we turn to the Reasoning Tasks:Dominance & ConsistencyEquivalence & SubsumptionOrderingReasoning tasks reduce to verifying properties of IPG Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.27The semantics of any ceteris paribus language can be represented in terms of properties of IPGSlide28
Reasoning Tasks
Dominance relation:α ≻ β iff there exists a sequence of flips from β to α Property to verify: Existence of path in IPG from β to α Consistency:A set of preferences is consistent if ≻ is a strict partial orderProperty to - verify: IPG is acyclicOrdering: ?Hint: The non-dominated alternatives in the IPG are the best
Strategy – Repeatedly Query IPG to get strata of alternativesEquivalence (& Subsumption):
A set
P
1
of
preferences is
equivalent
to another set P
2
if they induce the same dominance relation
Property to verify:
IPGs are reachability equivalent
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
28
semantics Slide29
Reasoning TasksRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
29Reasoning TaskComputation Strategy: Property of IPG to checkRemarksDominance: α ≻ β Is β reachable from α ?Consistency of a set of preferences (P)Is the IPG of P acyclic?
Satisfiability of the dominance relation; strict partial order Equivalence of two sets of preferences P1
and P
2
Ar
e the IPGs of P
1
and P
2
reachability-equivalent
?
Subsumption
of one set of preference (P
1
) by another (P
2
)
If
β
reachable
from
α
in
the IPG of P
1
, does the
same hold
in the IPG of P
2?
Ordering of alternativesIterative verification of the IPG for the non-existence of the non-dominated alternativesIterative modification of the IPG to obtain next set of non-dominated alternativesSlide30
Complexity of Dominance [Goldsmith et al. 2008]
Cast as a search for a flipping sequence, or a path in IPGα = (A = 1, B = 0, C = 0) β = (A = 0, B = 1, C = 1)α ≻ β – Why?
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
30
PSPACE-complete
Dominance testing reduces
to STRIPS
planning
(
Goldsmith et al
. 2008)Slide31
Complexity of Reasoning TasksRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
31Reasoning TaskComplexityWork by Dominance: α ≻ β PSPACE-completeGoldsmith et al. 2008Consistency of a set of preferences (P)PSPACE-completeGoldsmith et al. 2008Equivalence of
two sets of preferences P1 and P2PSPACE-completeSanthanam
et al. 2013
Subsumption
of one set of preference (P
1
) by another (P
2
)
PSPACE-complete
Santhanam
et al. 2013
Ordering
of alternatives
NP-hard
Brafman
et al.
2011Slide32
Part III – Practical AspectsPart III
Practical Aspects of Reasoning with Ceteris Paribus PreferencesRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.32Slide33
Practical AspectsPart III – Outline Two Sound
and Complete Reasoning Approaches:Logic ProgrammingAnswer Set Programming [Brewka et al. ]Constraint Programming [Brafman et al. & Rossi et al. ]Model Checking basedPreference reasoning can be reduced to verifying properties of the IPG [Santhanam et al. 2010]Translate IPG into a Kripke Structure ModelTranslate reasoning tasks into temporal logic properties over modelApproximation & Heuristics Wilson [Wilson 2006, 2011]
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
33Slide34
Preference Reasoning via Model CheckingThe
first practical solution to preference reasoning in moderate sized CP-nets, TCP-nets, CI-nets, etc.Casts dominance testing as reachability in an induced graphEmploys direct, succinct encoding of preferences using Kripke structuresUses Temporal logic (CTL, LTL) for querying Kripke structuresUses direct translation from reasoning tasks to CTL/LTL - Dominance Testing - Consistency checking (loop checking using LTL) - Equivalence and Subsumption Testing - Ordering (next-preferred) alternativesRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.34
Santhanam et al. (AAAI 2010, KR 2010,
ADT
2013);
Oster
et al. (ASE 2011, FACS 2012)Slide35
Model Checking [Clark et al. 1986]
Model Checking: Given a desired property , (typically expressed as a temporal logic formula), and a (Kripke) structure M with initial state s, decide if M, s ⊨ Active area of research in formal methods, AI (SAT solvers)Broad range of applications: hardware and software verification, security..Temporal logic languages : CTL, LTL, μ-calculus, etc.Many model checkers available : SMV, NuSMV, Spin, etc.Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.35
Advantages of Model Checking:
Formal Guarantees
Justification of ResultsSlide36
Preference Reasoning via Model CheckingKey Idea:
Overview of Approach Translate IPG into a Kripke Structure ModelTranslate reasoning tasks into verification of temporal logic properties on the modelRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.36Preference reasoning can be reduced to verifying properties of the Induced Preference Graph [Santhanam et al. 2010]Slide37
Overview: Preference Reasoning via Model CheckingRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
37AlternativesAttributes Preferences (Ceteris Paribus Statements)Temporal Logic Model Checker
Kripke
Structure
s
0
,
φ
Answer
K
P
ENCODE
TRANSLATE
Santhanam et al. AAAI 2010
States correspond to alternatives;
Transitions correspond to
flips (induced preferences)
Reasoning Task
(e.g.,
Dominance:
α ≻
β?)Slide38
Kripke Structure [Kripke, 1963
]A Kripke structure is a 4-tuple K=(S, S0, T, L) over variables V, whereS represents the set of reachable states of the systemS0 is a set of initial statesT represents the set of state transitionsL is labeling (interpretation) function maps each node to a set of atomic propositions AP that hold in the corresponding stateComputational tree temporal logic (CTL) is an extension of propositional logicIncludes temporal connectives that allow specification of properties that hold over states and paths in KExampleEF true in state s of K if holds in some state in some path beginning at sRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
38
Used to
specify labeled transition
systems describing states of
the world w.r.t. flow of timeSlide39
Encoding Preference SemanticsRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
39Let P = {pi} be a set of ceteris paribus preference statements on a set of preference variables X = {x
1, x2, …}Reasoning Strategy:
Construct a
Kripke
model K
P
=
(S, S
0
, T,
L) using variables Z
Z = {
z
i
| x
i
∈
X}, with each variable
z
i
having same domain D
i
as x
i
K
P
must mimic the IPG is some sense
The State-Space of K
P
S = : states correspond to set of all alternatives
T : transitions correspond to allowed changes in valuations according to flip-semantics of the languageL : labeling (interpretation) function maps each node to a set of atomic propositions AP that hold in the corresponding stateS0 : Initial states assigned according to the reasoning task at handSlide40
From Syntax to SemanticsRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
40Encode KP such that paths in IPG are enabled transitions, and no additional transitions are enabled
Let p be a conditional preference statement in Pp induces a flip between two nodes in the IPG iff“Condition” part in the preference statement is satisfied by both nodes
“Preference” part (less & more preferred valuations) in satisfied by both
“Ceteris Paribus” part that ensures apart from (1 & 2) that all variables other than those specified to change as per (2) are equal in both nodes
Create transitions in K
P
with guard conditions
“Condition” part of statement is translated to the
guard
condition
“Preference” part of statement is translated to assignments of variables in the target state
How to ensure ceteris paribus condition?Slide41
From Syntax to SemanticsRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
41Encode KP such that paths in IPG are enabled transitions, and no additional transitions are enabled
Let p be a conditional preference statement in Pp induces a flip between two nodes in the IPG iff“Condition” part in the preference statement is satisfied by both nodes
“Preference” part (less & more preferred valuations) in satisfied by both
“Ceteris Paribus” part that ensures apart from (1 & 2) that all variables other than those specified to change as per (2) are equal in both nodes
Create transitions in K
P
with guard conditions
“Condition” part of statement is translated to the
guard
condition
“Preference” part of statement is translated to assignments of variables in the target state
How
to encode ceteris paribus condition in the guards?Slide42
From Syntax to SemanticsRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
42E
quality of source and destination states forbidden as part of the guard condition specification!Workaround: Use auxiliary variables hi
to label edges
Auxiliary edge labels don’t contribute to the state space
Recall
: In temporal logics, destination
states represent
“
future
” state of the worldSlide43
From Syntax to SemanticsRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
43Guard condition specificationRecall: p induces a flip between two nodes in the IPG
iff“Condition” part in the preference statement is satisfied by both nodes
“Preference” part (less & more preferred valuations) in satisfied by both
“Ceteris Paribus” part that ensures apart from (1 & 2) that all variables other than those specified to change as per (2) are equal in both nodes
For each statement
p
of the form where is the “condition” part, guard condition is
condition
preference
ceteris paribusSlide44
Encoding CP-net semantics
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
44
Functional, LO, Unavailable
Functional, LO, Official f
ix
Functional, HI, Official fix
Functional, HI, Unavailable
Unproven, LO, Unavailable
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Unproven, HI, Official fix
Unproven, HI, Unavailable
p
1
p
2
p
2
p
2
p
2
p
1
p
1
p
1
p
3
p
3
F
E
A
E=Functional:
Unavailable
≻
Official fix
LO
≻
HI
Functional
≻
Unproven
Functional, LO, Unavailable
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ix
Functional, HI, Official fix
Functional, HI, Unavailable
Unproven, LO, Unavailable
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Unproven, HI, Unavailable
Direct & succinct
Kripke
Structure
Induced Preference
GraphSlide45
Encoding CP-net semanticsRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
Functional, LO, Unavailable
Functional, LO, Official f
ix
Functional, HI, Official fix
Functional, HI, Unavailable
Unproven, LO, Unavailable
Unproven, LO, Official fix
Unproven, HI, Official fix
Unproven, HI, Unavailable
F
E
A
E=Functional:
Unavailable
≻
Official fix
LO
≻
HI
Functional
≻
UnprovenSlide46
Encoding TCP-net SemanticsRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
46TCP-nets : Same overall idea as CP-netsAdditional rule for encoding simple relative importanceFunctional, LO, Unavailable
Functional, LO, Official f
ix
Functional, HI, Official fix
Functional, HI, Unavailable
Unproven, LO, Unavailable
Unproven, LO, Official fix
Unproven, HI, Official fix
Unproven, HI, Unavailable
F
E
A
E=Functional:
Unavailable
≻
Official fix
LO
≻
HI
Functional
≻
UnprovenSlide47
Encoding CP-theory SemanticsRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
47CP-theory: Same idea as TCP-net + Additional rule
Functional, LO, Unavailable
Functional, LO, Official f
ix
Functional, HI, Official fix
Functional, HI, Unavailable
Unproven, LO, Unavailable
Unproven, LO, Official fix
Unproven, HI, Official fix
Unproven, HI, Unavailable
F
E
A
E=Functional:
Unavailable
≻
Official fix
LO
≻
HI
Functional
≻
UnprovenSlide48
Encoding Reasoning Tasks as Temporal Logic Properties
Next : Specifying and Verifying Properties in Temporal Logic Translating Reasoning Tasks into Temporal Logic PropertiesRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.48Slide49
Encoding Reasoning Tasks as Temporal Logic Properties
Computational tree temporal logic (CTL) [Clark et al. 1986] is an extension of propositional logicIncludes temporal connectives that allow specification of properties that hold over states and paths in a Kripke structureCTL Syntax & Semantics Translating Reasoning Tasks into Temporal Logic PropertiesDominance TestingConsistencyEquivalence & Subsumption TestingOrdering alternativesRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.49
NuSMV
[
Cimatti
et al. 2001]
:
O
ur choice of model checker Slide50
Dominance Testing (via NuSMV)
Given outcomes α and β, how to check if α ≻ β ?Let ϕα be a formula that holds in the state corresponding to αLet ϕβ be a formula that holds in the state corresponding to βBy construction, α ≻ β wrt iff in the Kripke Structure KN : a state in which ϕβ holds is
reachable from a state in which ϕα
holds
α
≻
β
iff
the model checker
NuSMV
can verify
(SAT)
When
queried with
¬
(
),
if indeed
α
≻
β
, then model
checker
produces
a proof of
α
≻
β
(flipping sequence
)
Experiments show feasibility of method for 100 var. in secondsRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
50
Santhanam et al. AAAI 2010Slide51
Obtaining a Proof of Dominance
011 is preferred to 100 Improving flipping sequence: 100 →101 → 001 → 011Proof : 011 ≻ 001 ≻ 101 ≻ 100 Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.51
010
011
000
001
101
111
100
110
Santhanam et al. AAAI 2010
One of the proofs is chosen
non-deterministicallySlide52
Obtaining a Proof of Dominance
011 is preferred to 100 Improving flipping sequence: 100 →101 → 001 → 000 → 011Proof #2: 011 ≻ 000 ≻ 001 ≻ 101 ≻ 100
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
52
Santhanam et al. AAAI 2010
010
011
000
001
101
111
100
110Slide53
Non-dominance 011 is not preferred to 000 (if relative importance of B is not stated)
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.53010
011
000
001
101
111
100
110
Santhanam et al. AAAI 2010
010
011
000
001
101
111
100
110Slide54
Equivalence and Subsumption Testing
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.54
CTL Model
Checking
Santhanam et al. ADT 2013
Combined Induced
Preference Graph
P
1
P
2
δ(
P
1
)
δ(
P
2
)
δ(
P
1
, P
2
)
AnswerSlide55
Equivalence and Subsumption Testing
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.55Santhanam et al. ADT 2013
Combined Induced
Preference Graph
Kripke
Structure
State from
which verification is done
True
⇔
P
1
⊑
P
2
False
⇔
P
2
⋢
P
1
Model Checker returns → as proofSlide56
Equivalence and Subsumption TestingRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
56Santhanam et al. ADT 2013
Combined Induced
Preference Graph
Kripke
Structure
True
⇔
P
1
⊑
P
2
True
⇔
P
2
⊑
P
1
P
1
≡
P
2 Slide57
Ordering : Finding the Next-preferred AlternativeWhich alternatives are most-preferred (non-dominated)?
Can we enumerate all alternatives in order?Computing total and weak order extensions of dominance We verify a sequence of reachability properties encoded in CTLRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.57
010
011
000
001
101
111
100
110
1
2
3
4
5
How to deal with cycles?
Acyclic Case: Oster et al. FACS 2012Slide58
Part IV – ApplicationsPart IV
ApplicationsRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.58Slide59
ApplicationsSustainable Design of Civil Infrastructure (e.g., Buildings, Pavements)
Engineering Design (Aerospace, Mechanical)Strategic & mission critical decision making (Public policy, Defense, Security)Chemical and Nano-ToxicologySite Selection for Nuclear Waste and setting up new nuclear plantsSoftware EngineeringSemantic Search Code Search, Search based SEProgram Synthesis, OptimizationTest prioritizationRequirements EngineeringDatabases – Skyline queriesStable Marriage problemsAI Planning, configurationRecommender SystemsRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.59Slide60
Applications
Sustainable DesignRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.60Slide61
Applications
Sustainable DesignRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.61Slide62
Applications
Goal Oriented Requirements EngineeringRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.62
Oster et al. ASE 2011Slide63
Goal oriented Requirements Engineering – CI-nets
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.63
Oster et al. ASE 2011Slide64
Applications - Minimizing Credential DisclosureUser needs renter’s insurance for
new apartmentWhich service to choose to get a quote?Privacy issue – disclosure of sensitive credentialsAll services do the same tasks (from user’s perspective) info:User’s Preferences:P1. If bank account number is disclosed, then I would rather give my address than bank routing number to the serverP2. If I have to disclose my address but not my name, then I would prefer to give my bank routing number rather than my bank account numberP3. If I don’t need to disclose my bank account number, I will give my name and address instead of my bank routing number.Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.64
Oster et al. FACS 2012Slide65
Applications - Minimizing Credential DisclosureFinding a sequence of next-preferredSuboptimal sequence of preferred sets of credentials can
compromise privacy, when it could have been avoidedRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.65Oster et al. FACS 2012Slide66
Part V – ToolPart V
ToolRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.66Slide67
iPref-R Preference Reasoning Tool
α-version of iPref-R freely available at http://fmg.cs.iastate.edu/project-pages/preference-reasoner/http://fmg.cs.iastate.edu/project-pages/GUI-iPref-R/Demo http://fmg.cs.iastate.edu/project-pages/GUI-iPref-R/video/demo.htmlCurrently supports representing and reasoning with CI-netsCP-nets
Support for other languages in progressReasoning tasks supported
Dominance Testing
Consistency
Next-preferred (for acyclic CP/CI-nets)
Support for Equivalence & Subsumption testing coming
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
67Slide68
iPref-R Architecture
Architecture decouples preference reasoning from choice ofModel checkerTranslation of preference Preference languagesModular design enables extension to other ceteris paribus languages, reasoning tasks and encodingsTool DependenciesModel Checker – NuSMV or Cadence SMVJava Runtime Environment
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
68Slide69
iPref
-R Architecture
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
69
Justifier
Dominance
NuSMV
Model Checker
Consistency
Language
Preprocessor
Preferences in CP-net, TCP-net, CI-net, CP-theory, etc.
Query Preprocessor
Preference Reasoning tasks
(dominance/consistency/ordering/equivalence)
Result
Justification (proof of result)
Next-preferred
Equivalence
Subsumption
SMV model
Translators written in Java Slide70
iPref-R Architecture
Tool DependenciesModel Checker – NuSMV or Cadence SMVJava Runtime EnvironmentInput/OutputPreference specifications encoded in XMLTranslated to SMV (Kripke model encoding)Parsers to translate output of model checkerIterative process to compute alternatives in orderWorking implementation to demonstrate our approach (soon on our website)
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
70Slide71
Summary
Qualitative Preference LanguagesRepresentation : Syntax of languages CP-nets, TCP-nets, CI-nets, CP-TheoriesQualitative Preference LanguagesCeteris Paribus semantics: the induced preference graph (IPG)Reasoning: Consistency, Dominance, Ordering, Equivalence & SubsumptionComplexity of ReasoningPractical aspects: Preference Reasoning via Model CheckingFrom ceteris paribus semantics (IPG) to Kripke structures Specifying and verifying properties in temporal logicReasoning tasks reduce to verification of temporal propertiesRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
71Slide72
Summary
ApplicationsEngineering: Civil, Software (SBSE, RE, Services), Aerospace, ManufacturingSecurity: Credential disclosure, Cyber-securityAlgorithms: Search, Stable Marriage, Allocation, Planning, Recommender systemsEnvironmental applications: Risk Assessment, Policy decisions, Environmental impact, Computational SustainabilityiPref-RA general, practically useful Preference Reasoner for ceteris paribus languagesArchitectureDemoUse of iPref-R in Security, Software EngineeringRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.72Slide73
ReferencesRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
73Ganesh Ram Santhanam, Samik Basu and VasantHonavar. Verifying Preferential Equivalence & Subsumptionvia Model Checking.3rd International Conference on Algorithmic Decision Theory. 2013.Zachary Oster, Ganesh Ram Santhanam, Samik Basu and VasantHonavar. Model Checking of Qualitative Sensitivity Preferences to Minimize Credential Disclosure.International Symposium on Formal Aspects of Component Software (FACS) 2012.Ganesh Ram Santhanam, Samik Basu, VasantHonavar: Representing and Reasoning with Qualitative Preferences for Compositional Systems. J. Artif. Intell. Res. (JAIR) 2011.Ganesh Ram Santhanam Samik
Basu and VasantHonavar. Identifying Sustainable Designs Using Preferences over Sustainability Attributes. AAAI Spring Symposium: Artificial Intelligence and Sustainable Design 2011.Ganesh
Ram
Santhanam
, Zachary J. Oster,
Samik
Basu
: Identifying a preferred countermeasure strategy for attack
graphs.
CSIIRW
2013
Ganesh
Ram
Santhanam
,
Samik
Basu
and
VasantHonavar
.
Dominance Testing via Model Checking
. AAAI Conference on Artificial Intelligence 2010.
Ganesh
Ram
Santhanam
,
Samik
Basu and VasantHonavar. Efficient Dominance Testing for Unconditional Preferences
. International Conference on the Principles of Knowledge Representation and Reasoning 2010.Ganesh Ram Santhanam and KasthuriranganGopalakrishnan. Pavement Life-Cycle Sustainability Assessment and Interpretation Using a Novel Qualitative Decision Procedure. Journal of Computing in Civil Engineering 2013.
Zachary J. Oster, Ganesh Ram Santhanam, Samik Basu: Automating analysis of qualitative preferences in goal-oriented requirements engineering. ASE 2011.G. Brewka, M.
Truszczynski; S. Woltran. Representing Preferences Among Sets. AAAI 2010G. Brewka, I. Niemelä, M.
Truszczynski. Preferences and NonmonotonicReasoning, AI Magazine (special issue on preference handling) 2008.G.
Brewka. Complex Preferences for Answer Set Optimization, KR 2004.G. Brewka
. Answer Sets and Qualitative Decision Making, Synthese2005.G.
Brewka, I. Niemelä, T. Syrjänen. Logic Programs wirhOrdered
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, Computational Intelligence 2004.
Ronen
I.
Brafman
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Pilotto
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DomenicoSalvagnin
, Kristen Brent Venable, Toby Walsh:
The Next Best Solution
. AAAI 2011.
Ronen
I.
Brafman
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Domshlak
:
Preference Handling -An Introductory Tutorial
. AI Magazine 2009.
Maxim
Binshtok
, Ronen I.
Brafman
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Domshlak
, Solomon
EyalShimony
:
Generic Preferences over Subsets of Structured Objects
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.
Intell
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Brafman
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Domshlak
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EyalShimony: On Graphical Modeling of Preference and Importance. J. Artif. Intell. Res. (JAIR) 2006.Ronen I. Brafman, Carmel Domshlak, Solomon EyalShimony, Y. Silver: Preferences over Sets.AAAI 2006.Ronen I. Brafman, Yuri Chernyavsky: Planning with Goal Preferences and Constraints. ICAPS 2005.Slide74
ReferencesRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
74Craig Boutilier, Ronen I. Brafman, Carmel Domshlak, HolgerH. Hoos, David Poole: CP-nets: A Tool for Representing and Reasoning with Conditional Ceteris Paribus Preference Statements. J. Artif. Intell. Res. (JAIR) 2004.Carmel Domshlak, Ronen I. Brafman: CP-nets: Reasoning and Consistency Testing. KR 2002.Ronen I. Brafman, Carmel Domshlak: Introducing Variable Importance Tradeoffs into CP-Nets. UAI 2002.SotiriosLiaskos, Sheila A. McIlraith, ShirinSohrabi, John Mylopoulos: Representing and reasoning about preferences in requirements engineering.Requir. Eng. 2011.ShirinSohrabi, Jorge A. Baier, Sheila A. McIlraith
: Preferred Explanations: Theory and Generation via Planning. AAAI 2011.ShirinSohrabi, Sheila A. McIlraith: Preference-Based Web Service Composition: A Middle Ground between Execution and Search
. International Semantic Web Conference (1) 2010.
Jorge
A.
Baier
, Sheila A.
McIlraith
:
Planning with Preferences
. AI Magazine 2008.
Zachary
J. Oster:
Reasoning with qualitative preferences to develop optimal component-based systems
. ICSE 2013.
Judy
Goldsmith,
JérômeLang
,
MiroslawTruszczynski
,
NicWilson
:
The Computational Complexity of Dominance and Consistency in CP-Nets
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.
Intell
. Res. (JAIR) 2008.
Judy Goldsmith, Ulrich Junker: Preference Handling for Artificial Intelligence
. AI Magazine 2008.WalidTrabelsi, NicWilson, Derek G. Bridge: Comparative Preferences Induction Methods for Conversational Recommenders. ADT 2013NicWilson: Importance-based Semantics of Polynomial Comparative Preference Inference
. ECAI 2012.WalidTrabelsi, NicWilson, Derek G. Bridge, Francesco Ricci: Preference Dominance Reasoning for Conversational Recommender Systems: a Comparison between a Comparative Preferences and a Sum of Weights Approach.International Journal on Artificial Intelligence Tools 2011.MeghynBienvenu,
JérômeLang, NicWilson: From Preference Logics to Preference Languages, and Back. KR 2010Sylvain Bouveret, UlleEndriss, JérômeLang
: Conditional Importance Networks: A Graphical Language for Representing Ordinal, Monotonic Preferences over Sets of Goods.IJCAI 2009.Sylvain Bouveret
, UlleEndriss, JérômeLang: Fair Division under Ordinal Preferences: Computing Envy-Free Allocations of Indivisible Goods. ECAI 2010.
Francesca Rossi, Kristen Brent Venable, Toby Walsh: A Short Introduction to Preferences: Between Artificial Intelligence and Social Choice.
Synthesis Lectures on Artificial Intelligence and Machine Learning 2011.Ronen I. Brafman, Francesca Rossi, DomenicoSalvagnin
, Kristen Brent Venable, Toby Walsh:
Finding the Next Solution in Constraint-and Preference-Based Knowledge Representation Formalisms
. KR 2010.
Maria
Silvia
Pini
, Francesca Rossi, Kristen Brent Venable, Toby Walsh
: Stable marriage problems with quantitative preferences.
CoRRabs
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Francesca
Rossi, Kristen Brent Venable, Toby Walsh:
Preferences in Constraint Satisfaction and Optimization
. AI Magazine 2008. Slide75
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75Craig Boutilier, Ronen I. Brafman, Carmel Domshlak, HolgerH. Hoos, David Poole: CP-nets: A Tool for Representing and Reasoning with Conditional Ceteris Paribus Preference Statements. J. Artif. Intell. Res. (JAIR) 2004.Cristina Cornelio, Judy Goldsmith, Nicholas Mattei, Francesca Rossi, Kristen Brent Venable: Updates and Uncertainty in CP-Nets. Australasian Conference on Artificial Intelligence 2013: 301-312Umberto Grandi, Andrea Loreggia, Francesca Rossi, Vijay A. Saraswat: From Sentiment Analysis to Preference Aggregation. ISAIM 2014Minyi Li, Quoc Bao Vo, Ryszard Kowalczyk: Efficient heuristic approach to dominance testing in CP-nets. AAMAS 2011
Minyi Li, Quoc Bao Vo, Ryszard Kowalczyk
:
An Efficient Majority-Rule-Based Approach for Collective Decision Making with CP-Nets
. KR
2010
Toronto
Italy
Australia
Israel
Kentucky
Europe
USASlide76
Thank youTeam:
Ganesh Ram Santhanam, Samik Basu, Vasant HonavarOther CollaboratorsDr. Giora Slutzki Dr. Kasthurirangan GopalakrishnanDr. Robyn LutzDr. Zachary OsterCarl ChapmanKaterina MitchellAcknowledgementsNSF Grants IIS 0711356, CCF 0702758, CCF 1143734, CNS 1116050Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.76Slide77
Efficient Dominance Testing for Unconditional Preferences*
Approach – restrict the preference languageTUP-net = Unconditional fragment of TCP-netLess expressive, yet practically usefulIntroduce a new dominance relation (QBF) for TUP-netsDominance testing in TUP-nets = QBF SAT in polynomial timeCompare the new dominance relation with unconditional counterparts of TCP-nets, CP-nets*Santhanam, Basu, Honavar. KR 2010Type of Preference
CP-netTUP-netTCP-net
Unconditional Intra-variable preference
√
√
√
Unconditional Relative importance
√
√
Conditional
Intra-variable preference
√
√
Conditional
relative importance
√
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
77Slide78
Dominance for Unconditional Preferences
Approach – restrict the preference languageTUP-net = Unconditional fragment of TCP-netLess expressive, yet practically usefulIntroduce a new dominance relation (QBF) for TUP-netsDominance testing in TUP-nets = QBF SAT in polynomial time
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.
78Slide79
Properties of Dominance
Desirable – Strict Partial OrderIrreflexivity – Yes Transitivity – No!How to make dominance transitive?Restrict ⊳ to an interval orderInterval order – a partial order not containing 2 ⊕ 2 substructureRepresenting and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.79Slide80
Comparison of Semantics
Brafman et al.WilsonSanthanam et al.Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.80Slide81
Questions Tool demo
Representing and Reasoning with Qualitative Preferences - Ganesh Ram Santhanam, Iowa State University.81