Aucun titre de diapositive

1
Logical representation of preference
nonmonotonic reasoning Jérôme Lang Institut de
Recherche en Informatique de Toulouse CNRS -
Université Paul Sabatier - Toulouse (France)

• About the meaning of preference
• The need for compact representations and the
  role of logic
• Some logical languages for compact preference
• representation (a brief survey with examples)
• Preference representation and NMR
• Other issues

2

• About the meaning of preference
• The need for compact representations and the
  role of logic
• Some logical languages for preference
  representation
• Preference representation and NMR
• Other issues

3

• preference
• has different meanings in different communities
• in economics / decision theory
• preference relative or absolute satisfaction
• of an individual when facing
• various situations

4

• preference
• has different meanings in different communities
• in economics / decision theory
• preference relative or absolute satisfaction
• of an individual when facing
• various situations
•  
• in KR / NMR
• preference weak strict order
• with various meanings
• A is more plausible / believed than B 
• preferential models, preferential entailment
  etc.

5

•  preference 
• has different meanings in different communities
• in economics / decision theory
• preference relative or absolute satisfaction
• of an individual when facing
• various situations
•  
• in KR / NMR
• preference weak strict order
• with various meanings
• A is more plausible / believed than B 
• preferential models, preferential entailment
  etc.

relative (ordinal) uncertainty
control
6
Preference structure represents the preferences
of an agent over a set S of possible alternatives
7

• About the meaning of preference
• The need for compact representations the role
  of logic
• Some logical languages for preference
  representation
• Preference representation and NMR
• Other issues

8
Complex domains a state is defined by a tuple of
values for a given set of variables
Example preferences on airplane tikcets
option (destination, price, dates,
number-changes)
preferentially interdependent variables
Combinatorial explosion prohibitive number of
alternative
50 destinations, 10 price ranges, 10 departure
dates and 10 return dates, 0/1/2 changes
150 000 alternatives
Need for concise representations for preferences
9
Representation and elicitation of preferences
agent (user, client)
INTERACTIVE ELICITATION
concise form
REPRESENTATION
preference relation on S
preferred alternatives
10
Why (propositional) logic?

• prototypical compact structured language
• good starting point
• expressive power
• closeness to human intuition
• elicitation issues
• efficient and well-studied algorithms
• ( tractable fragments etc.)
• optimization issues (find optimal alternatives)

11

• About the meaning of preference
• The need for compact representations the role
  of logic
• A brief survey on propositional logical
  languages
• for preference representation
• Preference representation and NMR
• Other issues

12
Some logical languages for preference
representation
1a. Basic propositional representation
K propositional formula
set of possible alternatives
2 positions maximum to be filled 4 candidates
A,B,C,D K (? A ? ? B) ? (? A ? ?C) ? (?
A ? ?D) ? (? B ? ? C) ? (?B ? ?D) ? (? C
? ? D)
K ? 2 A, B, C, D
13
Some logical languages for preference
representation
1a. Basic propositional representation
K
B ?1, , ?n set of goals
 
K ? ?1 ? ? ?n
? such that ?
 good  states
? K
?
?
impossible states
K ? ? (?1 ? ? ?n )
? such that ?
 bad  states
14
Some logical languages for preference
representation
1a. Basic propositional representation
K ? 2 A, B, C, D G (A ? B), (B ? ?
C), ? D I would like to hire A or to
hire B if B is hired then I would prefer not
to hire C I would like not to hire D
 
(A,B, ? C, ? D) hire A and B (A, ? B, C, ?
D) hire A and C (A, ? B, ? C, ? D) hire A only (?
A,B, ? C, ? D) hire B only
 good  states
15
Some logical languages for preference
representation
1b. Basic propositional representation
cardinality
K

B ?1, , ?n set of goals
For all ? ? Mod(K), uB(?) i, ?
?i
 
16
Some logical languages for preference
representation
1b. Basic propositional representation
cardinality
K ? 2 A, B, C, D G (A ? B), (B
? ? C), ? D
u(?)3
 
?
u(?)2
?
u(?)1
17
Some logical languages for preference
representation
1c. Basic propositional representation
inclusion
K
B ?1, , ?n set of goals
 
For all ? , ?  ? Mod(K) ? ?
?  if and only if i , ?
?j
?i ? j , ? 
18
Some logical languages for preference
representation
1c. Basic propositional representation
inclusion
K ? 2 A, B, C, D G (A ? B), (B
? ? C), ? D
2
3
1
 
123
?
?
(A, D) (B, D)
?
?
2
19
Some logical languages for preference
representation
2. Propositional logic weights
K
B (?1, x1 ), , (?n , xn )
?I propositional formula
 
xi gt 0 reward
xi ??
xi lt 0 penalty
Example additive weights
For all ? ? Mod(K),
?
xi
uB(?)
i ? 1 .. N
?i
?
20
Some logical languages for preference
representation
2. Propositional logic weights
K
B (?1, x1 ), , (?n , xn )
?I propositional formula
 
xi gt 0 reward
xi ??
xi lt 0 penalty
Example additive weights
For all ? ? Mod(K),
other aggregation functions
?
xi
uB(?)
i ? 1 .. N
?i
?
21
Some logical languages for preference
representation
2. Propositional logic weights
K
B (?1, x1 ), , (?n , xn )
?I propositional formula
 
xi gt 0 reward
xi ??
xi lt 0 penalty
For all ? ? Mod(K),
uB(?) F ( xi , i ?
1 .. N )
?i
?
22
Some logical languages for preference
representation
2. Propositional logic weights
K
B (?1, x1 ), , (?n , xn )
?I propositional formula
 
xi gt 0 reward
xi ??
xi lt 0 penalty
For all ? ? Mod(K),
uB(?) F ( G ( xi ,
i ? 1 .. N, xi gt 0 ) , H ( xj
, i ? 1 .. N , xi lt 0 ) )
?j
?
bipolarity
23
Some logical languages for preference
representation
2. Propositional logic (additive) weights
K ? 3 A, B, C, D, E G (B ? C,
5) (A ? C, 6) (A ? B, -3) (D ? E,
-3) (D, 10) (E, 8) (A, 6) (B,
4) (C, 2)
only B and C can teach logic
only A and C can teach databases
A and B would be in the same group (to be avoided)
idem for D and E
D is the best candidate E is the second best etc.
24
Some logical languages for preference
representation
2. Propositional logic weights
? (A, D, E, ?B, ?C)
K ? 3 A, B, C, D, E G (B ? C,
5) (A ? C, 6) (A ? B, -3) (D ? E,
-3) (D, 10) (E, 8) (A, 6) (B, 4)
(C, 2)
6
-3
u(?) 27
10
8
6
25
Some logical languages for preference
representation
2. Propositional logic weights
? (C, D, E, ?A, ?D)
K ? 3 A, B, C, D, E G (B ? C,
5) (A ? C, 6) (A ? B, -3) (D ? E,
-3) (D, 10) (E, 8) (A, 6) (B, 4)
(C, 2)
5
6
u(?) 31
10
8
2
26
Some logical languages for preference
representation
2. Propositional logic weights
u(?)
?
K ? 3 A, B, C, D, E G (B ? C,
5) (A ? C, 6) (A ? B, -3) (D ? E,
-3) (D, 10) (E, 8) (A, 6) (B, 4)
(C, 2)
31
(C,D,E) (A,C,D) (A,B,D) (A,D,E)
(B,C,D) (A,C,E) (B,D,E) (C,D)
29
28
27
24
23
27
Some logical languages for preference
representation
3a. Propositional logic priorities
K
B1 Bp
B ? B1, , Bp ?
stratification of B
K ? 2 A, B, C, D, E
B1 B ? C, A ? C, ? (D ? E), ? (D ? E)
1
2
3
4
B2 D,A B3 E B4 B, C
5
6
7
8
9
28
3a. Propositional logic priorities
K ? 3 A, B, C, D, E
B1 B ? C, A ? C, ? (A ? B), ? (D ? E)
1
2
3
4
B2 D,A B3 E B4 B, C
5
6
7
8
9
 Best-out  ordering u (?) min
i, ? violates at least a formula of Bi
( ? if there is no such i)
29
3a. Propositional logic priorities
? (A, B, C, ?D, ?E)
K ? 3 A, B, C, D, E
B1 B ? C, A ? C, ? (A ? B), ? (D ? E)
1
2
3
4
u (?) 1
B2 D, A B3 E B4 B, C
5
6
7
8
9
 Best-out  ordering u (?) min
i, ? violates at least a formula of Bi
30
3a. Propositional logic priorities
? (A, C, D, ?B, ?E)
K ? 3 A, B, C, D, E
B1 B ? C, A ? C, ? (A ? B), ? (D ? E)
1
2
3
4
u (?) 3
B2 D,A B3 E B4 B, C
5
6
7
8
9
 Best-out  ordering u (?) min
i, ? violates at least a formula of Bi
31
3a. Propositional logic priorities
K ? 2 A, B, C, D, E
B1 B ? C, A ? C, A ? B, D ? E
1
2
3
4
B2 D B3 A,E B4 B,C
5
6
7
8
9
 leximin ordering
Benferhat et al. 93
w gt w iff (w satisfies more formulas of B1
than w) or (w and w satisfy the same
number of formulas of B1, and w
satisfies more formulas of B2 than w) or (w
et w satisfy the same number of formulas of B1
and of B2, and w satisfies more formulas of B3
than w) etc.
32
3a. Propositional logic priorities leximin
ordering
K ? 2 A, B, C, D, E
B1 B ? C, A ? C, A ? B, D ? E
1
2
3
4
B2 D B3 A,E B4 B,C
5
6
7
8
9
B1
B2
B3
B4
(A,C)
3
0
1
1
1
1
0
(A,D)
3
(B,C)
3
0
0
2
(C,D)
3
1
0
1
33
3a. Propositional logic priorities leximin
ordering
K ? 2 A, B, C, D, E
B1 B ? C, A ? C, A ? B, D ? E
1
2
3
4
B2 D B3 A,E B4 B,C
5
6
7
8
9
B1
B2
B3
B4
(A,C)
3
0
1
1
1
1
0
(A,D)
3
(B,C)
3
0
0
2
(C,D)
3
1
0
1
(D,E)
1
1
1
0
34
3a. Propositional logic priorities leximin
ordering
K ? 2 A, B, C, D, E
B1 B ? C, A ? C, A ? B, D ? E
1
2
3
4
B2 D B3 A,E B4 B,C
5
6
7
8
9
B1
B2
B3
B4
(A,C)
3
0
1
1
1
1
0
(A,D)
3
(B,C)
3
0
0
2
(C,D)
3
1
0
1
(D,E)
1
1
1
0
35
3a. Propositional logic priorities leximin
ordering
K ? 2 A, B, C, D, E
B1 B ? C, A ? C, A ? B, D ? E
1
2
3
4
B2 D B3 A,E B4 B,C
5
6
7
8
9
B1
B2
B3
B4
(A,C)
3
0
1
1
1
1
0
(A,D)
3
(B,C)
3
0
0
2
(C,D)
3
1
0
1
(D,E)
1
1
1
0
36
Some logical languages for preference
representation
3b. Propositional logic ordered disjunction
K
Brewka, Benferhat Le Berre 02
Y (j1 ? j2 ? jp ) ideally j1 otherwise
(sub-ideally) j2 otherwise j3 etc.
B ? Y1, , Yp ?
37
Some logical languages for preference
representation
3b. Propositional logic ordered disjunction
K
Y (j1 ? j2 ? jp ) ideally j1 otherwise
(sub-ideally) j2 otherwise j3 etc.
For all ? ? Mod(K),
j1
disu(?, Y) 0 if ?
? j1 ? ? ? ji-1 ? ji
i if ?
p1 if ?
? j1 ? ? ? jn
38
Some logical languages for preference
representation
3b. Propositional logic ordered disjunction
K
B ? Y1, , Yp ?
disu (?, B) ? disu (?, Y1), , disu (?, Yp) ?
39
Some logical languages for preference
representation
3b. Propositional logic ordered disjunction
K
B ? F1, , Fp ?
K ? 2 A, B, C, D, E
? (A,E) ? (A,B)
F1 (B ? C) ? (B ? C) 3 2 F2
(A ? C) ? (A ? C) 2 2 F3 ? (D ?
E) 1 1 F4 ? (A ? B) 1 2 F5
D ? A ? E ? B ? C 2 2 F5 ( 2
A,B,C,D,E) ? ( 2 A,B,C,D,E) 1 1
40
Some logical languages for preference
representation
3b. Propositional logic ordered disjunction
K
B ? F1, , Fp ?
gtB
K ? 2 A, B, C, D, E
? (A,E) ? (A,B)
F1 (B ? C) ? (B ? C) 3 2 F2
(A ? C) ? (A ? C) 2 2 F3 ? (D ?
E) 1 1 F4 ? (A ? B) 1 2 F5
D ? A ? E ? B ? C 2 2 F5 ( 2
A,B,C,D,E) ? ( 2 A,B,C,D,E) 1 1
41
3. Propositional logic priorities
K ? 2 A, B, C, D, E
B1 B ? C, A ? C, A ? B, D ? E
1
2
3
4
B2 D B3 A,E B4 B, C
5
6
7
8
9
 discrimin ordering
Brewka 89
strict inclusion
w gt w iff j ? B1, w satisfies j ? j
? B1, w satisfies j or ( j ? B1, w
satisfies j j ? B1, w satisfies j and
j ? B2, w satisfies j ? j ? B2, w
satisfies j ) etc.
42
3. Propositional logic priorities discrimin
ordering
K ? 2 A, B, C, D, E
B1 B ? C, A ? C, A ? B, D ? E
1
2
3
4
B2 D B3 A,E B4 B,C
5
6
7
8
9
B1
B2
B3
B4
-
6-
9
(A,C)
123-
(B,C)
-
--
89
123-
(A,D)
5
--
9
-234
(C,D)
5
--
9
12-4
43
3. Propositional logic priorities discrimin
ordering
K ? 2 A, B, C, D, E
B1 B ? C, A ? C, A ? B, D ? E
1
2
3
4
B2 D B3 A,E B4 B,C
5
6
7
8
9
B1
B2
B3
B4
-
6-
9
(A,C)
123-
(B,C)
-
--
89
123-
(A,D)
5
--
9
2--4
(C,D)
5
--
9
12-4
44
3. Propositional logic priorities discrimin
ordering
K ? 2 A, B, C, D, E
B1 B ? C, A ? C, A ? B, D ? E
1
2
3
4
B2 D B3 A,E B4 B,C
5
6
7
8
9
B1
B2
B3
B4
-
6-
-9
(A,C)
123-
(B,C)
-
--
89
123-
(A,D)
5
6-
--
-234
(C,D)
5
--
-9
12-4
45
3. Propositional logic priorities discrimin
ordering
K ? 2 A, B, C, D, E
B1 B ? C, A ? C, A ? B, D ? E
1
2
3
4
B2 D B3 A,E B4 B,C
5
6
7
8
9
B1
B2
B3
B4
incomparable
-
6-
-9
(A,C)
123-
(B,C)
-
--
89
123-
(A,D)
5
6-
--
-234
(C,D)
5
--
-9
12-4
46
3. Propositional logic priorities discrimin
ordering
K ? 2 A, B, C, D, E
B1 B ? C, A ? C, A ? B, D ? E
1
2
3
4
B2 D B3 A,E B4 B,C
5
6
7
8
9
B1
B2
B3
B4
leximin discrimin best-out
no
-
6-
-9
(A,C)
123-
yes
yes
(B,C)
-
--
89
123-
yes
no
no
(A,D)
5
6-
--
-234
yes
yes
yes
yes
yes
no
(C,D)
5
--
-9
12-4
47
Some logical languages for preference
representation
4. Propositional logic distances

• K

• B ? ?1, , ?p ?

• d S ? S ? ?
• d (?, ?) d (?, ?)
• d (?, ?) 0 iff ? ?
• (example d Hamming distance)
• d (?, ?i ) min (?, ?) ? satisfies K ? ?i
  
• d (?, B) F (d (?, ?1), d (?, ?2), , d (?, ?n)
  )
• ? ? ? iff d (?, B) ? d (?, B)

distance-based merging
48
Some logical languages for preference
representation
5.  ceteris paribus  preferences
von Wright 63 Hansson 66 Doyle Wellman 91
g j gt y
For any two states w, w such that - w satisfies
g ? j ? ?y - w satisfies g ? ? j ? y - w and
w coincide on  irrelevant  variables then ? gtB
? ( transitive closure)
49
Some logical languages for preference
representation
5.  ceteris paribus  preferences
g j gt y
For any two states w, w such that - w satisfies
g ? j ? ?y - w satisfies g ? ? j ? y - w and
w coincide on  irrelevant  variables then ? gtB
? ( transitive closure)
e.g.
variables outside Var (g) ? Var (j) ? Var (y)
(more sophisticated definitions are possible)
50
5.  ceteris paribus  preferences
K ? (coffee ? tea)
B coffee sugar gt ? sugar tea ? sugar gt
sugar T coffee gt tea gt ? coffee ? ?
tea T croissant gt ? croissant
(coffee, sugar, croissant)
(coffee, sugar, ?croissant)
(coffee, ?sugar, croissant)
(coffee, ?sugar, ?croissant)
(tea, ?sugar, croissant)
(tea, ?sugar, ?croissant)
(tea, sugar, croissant)
(tea, sugar, ?croissant)
(?coffee, ?tea, ?, croissant)
(?coffee, ?tea, ?, ?croissant)
51
Some logical languages for preference
representation
5.  ceteris paribus  preferences CP-nets
Boutilier et al. 99 Brafman Domshlak 02 ...

• variables stuctured in a network
• restriction on syntax

g (xa) gt (xa)
where the variables appearing in g are parents of
x in the network
52
5.  ceteris paribus  preferences CP-nets
country
53
5.  ceteris paribus  preferences CP-nets
country
JANUARY INDIA gt BRAZIL gt TURKEY gt RUSSIA
54
5.  ceteris paribus  preferences CP-nets
JANUARY INDIA gt BRAZIL gt TURKEY gt RUSSIA
Given two states o,o such that - departure in
January for o and o - destination(o) INDIA,
destination(o) BRAZIL - o and o coincide on
all other variables Ceteris paribus, in January
I prefer to go to India than to Brazil, to Brazil
than to Turkey etc. 
55
5.  ceteris paribus  preferences CP-nets
country
56
5.  ceteris paribus  preferences CP-nets
country
RUSSIA ST-PETERSBURG gt MOSCOW INDIA NEW-DELHI
gt MADRAS gt CALCUTTA ...
57
5.  ceteris paribus  preferences CP-nets
duration of stay
country
DURATION lt 10 DAYS TURKEY gt RUSSIA gt INDIA ?
BRAZIL ...
58
5.  ceteris paribus  preferences CP-nets
country
59
Some logical languages for preference
representation
6. Conditional desires
D (? ?) in context ?, ideally ? is true
Boutilier 94
R preference relation (complete preorder)
R satisfies D (? ?) iff Max (Mod (?), R) ?
Mod(?)
Intuitively the best states satisfying ?
satisfy ? too or equivalently the best states
satisfying ? ?? are better than the best states
satisfying ? ? ? ?
60
6. Conditional desires
R satisfies D (? ?) iff Max (Mod (?), R) ?
Mod(?)
D(coffee end-dinner) D(? coffee end-dinner ?
? cigarettes)
For instance
(end-dinner, coffee, cigarettes)
(end-dinner, coffee, ? cigarettes)
61
6. Conditional desires
R satisfies D (? ?) iff Max (Mod (?), R) ?
Mod(?)
D(coffee end-dinner) D(? coffee end-dinner ?
? cigarettes)
For instance
(end-dinner, coffee, cigarettes)
(end-dinner, coffee, ? cigarettes)
62
6. Conditional desires
R satisfies D (? ?) iff Max (Mod (?), R) ?
Mod(?)
D(coffee end-dinner) D(? coffee end-dinner ?
? cigarettes)
For instance
(end-dinner, coffee, cigarettes)
(end-dinner, coffee, ? cigarettes)
63
6. Conditional desires
 Drowning effect
D(coffee end-dinner) D(? coffee end-dinner
? ? cigarettes) D(dessert end-dinner)
.
64
6. Conditional desires
 Drowning effect
D(coffee end-dinner) D(? coffee end-dinner
? ? cigarettes) D(dessert end-dinner)
incomparable !
.
65
6. Conditional desires
 Drowning effect
D(coffee end-dinner) D(? coffee end-dinner ?
? cigarettes) D(dessert end-dinner)
The lack of cigarettes  inhibits  the desire
for coffee but the desire for dessert as well
( inheritance blocking )
need to be improved
Lang 96 Lang, van der Torre Weydert 02
66
More references about logical preference
representation can be found in the
paper Coste-Marquis, Lang, Liberatore
Marquis, KR04
Expressive power and succinctness of
propositional languages for preference
representation
67

• About the meaning of preference
• The need for compact representations the role
  of logic
• A brief survey on propositional logical
  languages
• for preference representation
• Preference representation and NMR
• Other issues

68
Preference representation and NMR
1. Preference representation makes use of
default preferential independence between
variables
As long as no preferential dependence
between variables a and b was not explicitely
stated, they are considered as preferentially
independent
I prefer coffee to tea
(coffee, ? sugar) gt (tea, ? sugar) as long as no
interaction between drinks and sugar is specified
69
Preference representation and NMR
1. Preference representation makes use of
default preferential independence between
variables
As long as no preferential dependence
between variables a and b was not explicitely
stated, they are considered as preferentially
independent
birds fly
red birds by as long as no interaction between
flying and colour is specified
70
Preference representation and NMR
2. Are the preference representation languages
given in this overview monotonic or nonmonotonic
?

• the preference relation induced by B satisfies ?
  gt ?
• B ? B 
• ? does the preference relation induced by B
• satisfy ? gt ? ?

71
Preference representation and NMR
2. Are the preference representation languages
given in this overview monotonic or nonmonotonic
?

• the preference relation induced by B satisfy ? gt
  ?
• B ? B 
• ? does the preference relation induced by B
• satisfy ? gt ? ?

YES for ceteris paribus statements (and
CP-nets) NO for almost all other languages
72
Preference representation and NMR
2. Are the preference representation languages
given in this overview monotonic or nonmonotonic
?
I prefer a to be true if b then I prefer c to be
true
?abc
ceteris paribus preferences monotonic and
cautious
73
Preference representation and NMR
2. Are the preference representation languages
given in this overview monotonic or nonmonotonic
?
I prefer a to be true if b then I prefer c to be
true
abc, a?bc, a?b?c
?abc, ?a?bc, ?a?b ?c
ab?c
?ab?c
74
Preference representation and NMR
2. Are the preference representation languages
given in this overview monotonic or nonmonotonic
?
I prefer a to be true if b then I prefer c to be
true
abc, a?bc, a?b?c
?abc, ?a?bc, ?a?b ?c, ab?c
?ab?c
75
Preference representation and NMR
3. Hidden uncertainty in the expression of
preference (normality and preference)
Lang, van der Torre Weydert 03
76
Hidden uncertainty in the expression of
preference (normality and preference)
N(? ?)  normally ? if ? 
M ?RN, RP? satisfies N(? ?) ssi Max (Mod (?),
RN) ? Mod(?)
in the most normal ( typical ) states among
those where ? is true, ? is true as well.
...
77
Hidden uncertainty in the expression of
preference (normality and preference)
P(? ?)  I prefer ? if ? 
M ?RN, RP? satisfies D(? ?) iff Max (Max
(Mod (?), RN), RP) ? Mod(?)
the preferred states among those where ? is
true satisfy ?
the most normal states where ? ? ? is true are
preferred to the most normal states where ? ? ?
? is true
...
78
Hidden uncertainty in the expression of
preference (normality and preference)
1. I would like an ticket to Rome 2. I would like
a ticket to Amsterdam 3. I would not like having
both a ticket to Rome and a ticket to
Amsterdam 4. In the actual situation, I do not
have any ticket to Rome nor to Amsterdam.
D(r)
D(a)
? D(r ? a)
N(?r) N(?a)
...
79
Hidden uncertainty in the expression of
preference (normality and preference)
RP
RN
(? r,a)
(r,? a)
(? r, ? a)
(? r,a)
(r,? a)
(? r, ? a)
(r,a)
(r,a)
80
Hidden uncertainty in the expression of
preference (normality and preference)
RP
RN
(? r,a)
(r,? a)
(? r, ? a)
(? r,a)
(r,? a)
(? r, ? a)
(r,a)
(r,a)
81
Hidden uncertainty in the expression of
preference (normality and preference)
RP
RN
(? r,a)
(r,? a)
(? r, ? a)
(? r,a)
(r,? a)
(? r, ? a)
(r,a)
(r,a)
82
Hidden uncertainty in the expression of
preference (normality and preference)
D(? (r ? a))
RP
RN
(? r,a)
(r,? a)
(? r, ? a)
(? r,a)
(r,? a)
(? r, ? a)
(r,a)
(r,a)
83
Hidden uncertainty in the expression of
preference (normality and preference)
RP
RN
(? r,a)
(r,? a)
(? r, ? a)
(? r,a)
(r,? a)
(? r, ? a)
(r,a)
(r,a)
84
Preference representation and NMR
4. From belief change to preference change
Does it make sense to revise / update preferences
?
85
Preference representation and NMR
4. From belief change to preference change
a. revision of beliefs about preferences by
preferences
86
Preference representation and NMR
4. From belief change to preference change
a. revision of beliefs about preferences by
preferences
A Id like to have a Berliner Weisse, please B
with green syrup or with red syrup? A no syrup
please, thanks
Bs beliefs about As preferences
after
before
pure gt green gt red or pure gt red gt green or
pure gt red ? green
green gt red gt pure or red gt green gt pure or
red ? green gt pure
87
Preference representation and NMR
4. From belief change to preference change
b. XXXX of preferences by facts
88
Preference representation and NMR
4. From belief change to preference change
b. XXXX of preferences by facts
from a discussion with K. Konczak
A would you prefer to give your talk on monday
or tuesday? B well, rather on tuesday A I
just learned that the pope is visiting the lab
on monday (so that he can attend talks on
monday) B then I prefer to give the talk on
monday
89
Preference representation and NMR
4. From belief change to preference change
b. XXXX of preferences by facts
did the preference change?
depends on the granularity of the language
pope in the language (tuesday, pope) gt
(monday, pope) gt (tuesday, ?pope) gt (monday,
?pope)
pope not in the language tuesday gt monday
90
Preference representation and NMR
4. From belief change to preference change
b. XXXX of preferences by facts
did the preference change?
depends on the granularity of the language
pope in the language (tuesday, pope) gt
(monday, pope) gt (tuesday, ?pope) gt (monday,
?pope)
pope not in the language tuesday gt monday
focusing on the most normal situations
91
Preference representation and NMR
4. From belief change to preference change
b. XXXX of preferences by facts
did the preference change?
depends on the granularity of the language
pope in the language (tuesday, pope) gt
(monday, pope) gt (tuesday, ?pope) gt (monday,
?pope)
pope not in the language monday gt tuesday
after learning that the pope is visiting the lab
on monday
92
Preference representation and NMR
4. From belief change to preference change

c. temporal change of preferences
sushis gt walk
3 plates of sushis later
walk gt sushis
did preference change?
93
Preference representation and NMR
4. From belief change to preference change
c. temporal change of preferences
did the preference change?
depends once again on the granularity of the
language!
? full sushis gt walk full walk gt sushis
Preferences seem to be much more static than
beliefs
94

• About the meaning of preference
• The need for compact representations the role
  of logic
• A brief survey on propositional logical
  languages
• for preference representation
• Preference representation and NMR
• Other issues

95
Logical representation of more sophisticated
preferences
1. Variables with numerical domains (or even
continuous)
preference
sushis
5
10
15
20
but prefers a few sushis less if there is green
tea ice-cream on the menu
using fuzzy (ordinal or cardinal) quantities /
quantifiers
96
Logical representation of more sophisticated
preferences
1. Variables with numerical domains (or even
continuous)
Extending existing languages? Probably easier
for - (functional) weights - distances than
with - priorities - conditionals - ceteris
paribus statements
97
Logical representation of more sophisticated
preferences
2. Temporal preferences
cf. Delgrande, Schaub Tompits, KR2004
t
work
gt
t
work
sushis
gt
t
98
Logical representation of more sophisticated
preferences
2. Temporal preferences
Id like to have three coffee breaks today but
with some regularity
gt
gt
gt
gt
99
Logical representation of more sophisticated
preferences
3. Integrating ordinal and cardinal preference
compact representation of fuzzy relations
over propositional domains
mP 2VAR ? 2VAR ? 0,1
mP(w,w) ? 0,1 degree to which x is at least as
good as y
some assumptions that may be imposed (or
not) such as
transitivity mP(w,w) ? min (mP(w,w),
mP(w,w))
100
Logical representation of more sophisticated
preferences
3. Integrating ordinal and cardinal preference
compact representation of fuzzy relations
over propositional domains
(partial) weak order
mP(w,w) ? 0,1
complete weak order
mP(w,w) ? 0,1 mP(w,w) mP(w,w) ? 1
utility function
mP(w,w) mP(w,w) ( u(w)) for all w,w,w
101
Logical representation of more sophisticated
preferences
3. Integrating ordinal and cardinal preference
compact representation of fuzzy relations
over propositional domains
Can existing representation languages for
ordinal / cardinal preferences be integrated /
extended so as to represent fuzzy relations over
alternatives?
102
Logical representation of more sophisticated
preferences
4. Epistemic preferences
cf. Isaac Levi s epistemic utilities
gt preference relation over belief states u set
of belief states ? ?

• can be action-directed
• - Id like to know where the nearest sushi place
  is
• - I d like to know if there is already sugar in
  my coffee
• - John wants to know whether Mary still loves him

103
Logical representation of more sophisticated
preferences
4. Epistemic preferences
gt preference relation over belief states u set
of belief states ? ?

• can be action-directed
• or not
• - Id like to know why the British drive left
• - but Id prefer to know who won Roland-Garros

104
Logical representation of more sophisticated
preferences
4. Epistemic preferences
gt preference relation over belief states u set
of belief states ? ?

• can be action-directed
• or not
• - I dont want to learn whether I passed the exam
  or not
• before Im back from my holiday
• - I learn that I passed the exam
• gt I keep on ignoring whether I passed the
  exam
• gt I learn that I failed the exam

105
Logical representation of more sophisticated
preferences
5. Preferences involving other agents

• preferences about others epistemic state

John would prefer the fishy man behind him keep
on ignoring his credit card secret code Mary
would like John to know that she loves him but
before all she does not want Peter to learn about
that Mary would like John to have a
not-too-strong belief that she loves him (and
prefers a state where John does not have any clue
to a state where he is fully sure that she loves
him).
106
Logical representation of more sophisticated
preferences
5. Preferences involving other agents

• preferences about others epistemic state
• preferences about others preferences

John prefers a state where Mary prefers to marry
him to a state where she prefers to marry Peter
107
Logical representation of more sophisticated
preferences
5. Preferences involving other agents

• preferences about others epistemic state
• preferences about others preferences

COMPACT REPRESENTATION ?
108
Going further than compact representation
1. Bridging preference representation,
elicitation, and optimization
109
Going further than compact representation
1. Bridging preference representation,
elicitation, and optimization 2. Integrating
preference representation languages with
uncertainty representation languages ?
decision under uncertainty
110
Going further than compact representation
1. Bridging preference representation,
elicitation, and optimization 2. Integrating
preference representation languages with
uncertainty representation languages ?
decision under uncertainty 3. Logical preference
representation social choice a. preference
representation merging

• aggregating logically-expressed individual
  preferences
• (existing approaches to merging ? only for
  simple
• preference representation languages
• logical view of manipulation and
  strategyproofness
• Everaere, Konieczny Marquis, KR2004

111
Going further than compact representation
1. Bridging preference representation,
elicitation, and optimization 2. Integrating
preference representation languages with
uncertainty representation languages ?
decision under uncertainty 3. Logical preference
representation social choice a. preference
representation merging b. application to
fair division c. application to vote
112
Going further than compact representation
1. Bridging preference representation,
elicitation, and optimization 2. Integrating
preference representation languages with
uncertainty representation languages ?
decision under uncertainty 3. Logical preference
representation social choice a. preference
representation merging b. application to
fair division c. application to vote
113
3. Logical preference representation fair
division ( combinatorial auctions)

• A 1,, N set of agents
• G g1, , gp set of indivisible goods
• Find a fair division
• D G ? A
• given
• some constraints on feasible divisions
• the preferences of the agents
• some fairness of efficiency criteria

Needs compact preference representation!
114
3. Logical preference representation fair
division
? 2G ? A
Dependencies (non-additivity of ?)
A, B, C disjoints subsets of G and A gt B ? (A ?
C) gt (B ? C)
additivity
coffee ??? cookie
115
3. Logical preference representation fair
division
? 2G ? A
Dependencies (non-additivity of ?)
A, B, C disjoints subsets of G and A gt B ? (A ?
C) gt (B ? C)
additivity
coffee gt cookie coffee, tea ???
cookie, tea
116
3. Logical preference representation fair
division
? 2G ? A
Dependencies (non-additivity of ?)
A, B, C disjoints subsets of G and A gt B ? (A ?
C) gt (B ? C)
additivity
coffee gt cookie coffee, tea lt cookie,
tea
positive synergy between tea and cookie and/or
negative synergy between tea and coffee
117
Going further than compact representation
1. Bridging preference representation,
elicitation, and optimization 2. Integrating
preference representation languages with
uncertainty representation languages ?
decision under uncertainty 3. Logical preference
representation social choice a. preference
representation merging b. application to
fair division c. application to vote