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Reasoning about controllable and uncontrollable variables. Souhila KACI CRIL-CNRS Lens. Leendert van der Torre ILIAS Luxembourg. Preference reasoning. Logics of preferences attract much attention in KR Application: qualitative decision making

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reasoning about controllable and uncontrollable variables

Reasoning about controllable and uncontrollable variables

Souhila KACI

CRIL-CNRS

Lens

Leendert van der Torre

ILIAS

Luxembourg

Lamsade DIMACS

preference reasoning
Preference reasoning
  • Logics of preferences attract much attention in KR
  • Application: qualitative decision making
  • Algorithms used in some non-monotonic preference logics are too simple to be used in KR and reasoning applications
    • min/max specificity principles

Lamsade DIMACS

reasoning about preferences

mod(),’mod(),

>’

strong reas.

mod(),’mod(),

>’

optimistic reas.

’mod(), mod()

>’

pessimistic reas.

Reasoning about preferences

 > 

I prefer  to 

Our aim: to compute a total pre-order  on 

Lamsade DIMACS

example

3, 7

1, 2, 3,

6, 7

3, 6, 7

0, 1, 2

0, 1, 2,

4, 5

0, 4, 5

4, 5, 6

Example

{2,3,6,7}>{0,1,4,5}

{1,3}>{0,2}

  • P = {b > b, s  c > s  c}
  •  = {0: sbc, 1: sbc, 2: sbc, 3: sbc, 4: sbc, 5: sbc, 6: sbc, 7: sbc}
  • Different preference relations may be consistent with preferences

opt. reas.

strong reas.

pess. reas.

Lamsade DIMACS

min max specificity principles
min/max specificity principles
  • both compute the most compact preference relation

min

max

an alternative is considered

to be satisfactory as much

as there is no other alternatives

that are considered to be better

an alternative is considered

to be unsatisfactory as much

as there is no other alternatives

that are considered to be worse

Lamsade DIMACS

opt pess preferences controllable uncontrollable variables
Opt./Pess. preferences & controllable/uncontrollable variables
  • minimal specificity principle  gravitation towards the ideal  the best will hold for the alternatives  optimistic reasoning on preferences  controllable variables
  • maximal specificity principle  gravitation towards the worst  the worst will hold for the alternatives  pessimistic reasoning on preferences  uncontrollable variables

Lamsade DIMACS

contr uncontr variables qualitative decision theory
Contr./Uncontr. variables & Qualitative decision theory
  • states, actions, consequences
  • state variables:
    • observable variables  controllable variables
    • unobservable variables  uncontrollable variables
  • actions: controllable variables

Lamsade DIMACS

preferences in qualitative decision theory
Preferences in qualitative decision theory
  • hypothesis: all state variables are unobservable  uncontrollables
  • preferences on states, actions
  • preferences on consequences

Lamsade DIMACS

how can we use min max specificity algorithms
How can we use min/max specificity algorithms?
  • : the set of worlds on contr./uncontr. variables
  • minimal specificity principle on preferences based on controllable variables  optimistic reasoning  c
  • maximal specificity principle on preferences based on uncontrollable variables  pessimistic reasoning  u
  • merging c and u

Lamsade DIMACS

merging optimistic and pessimistic preferences
Merging optimistic and pessimistic preferences

O = {x>y, y>z,…}

P = {p>q, q>r,…}

step 1

step 2

x

p

q

y

Distinguished

Pre-orders

z

r

step 3

xp

xq , yp

Lamsade DIMACS

xr , yq , zp

some merging operators
Some merging operators
  • c = ({mp , mp} , {mp , mp})
  • u = (mp , mp} , {mp , mp})
  • Symmetric mergers
    • c =(E1, …, En), u =(E\'1, …, E\'m)
      •  = (E\'\'1, …, E\'\'n+m-1) = ({mp} , {mp, mp} , {mp})
  • Dictators
    • minmax: 1>2 iff 1>c2 or (1c2 and 1>u2)
      •  = ({mp} , {mp} , {mp} , {mp})
    • maxmin: 1>2 iff 1>u2 or (1u2 and 1>c2)
      •  = ({mp} , {mp} , {mp} , {mp})

Lamsade DIMACS

is this merging process satisfactory
Is this merging process satisfactory?
  • Not really…
  • interaction between controllable and uncontrollable variables is not possible…
  • Example:

If my boss accepts to pay the conference fee then I will work hard to finish the paper

  • conditional preferences

Lamsade DIMACS

optimistic conditional preference specification
Optimistic conditional preference specification
  • qi  LU, xi, yi  LC

O= {qi( xiyi)},

  • q  (xy) = (q  x) (q  y)
  • O = {(qi xi) (qi yi)}
  • o following the minimal specificity principle

Lamsade DIMACS

pessimistic conditional preference specification
Pessimistic conditional preference specification
  • xi  LC, qi , ri  LU,

O= {xi( qiri)},

  • x  (qr) = (x  q) (x  r)
  • O = {(xi qi) (xi ri)}
  • p following the maximal specificity principle

Lamsade DIMACS

example1
Example
  • O = {money(work > work), money(work > work), money  (project > project)}
    • o = ({mwp, mwp, mwp} , {mwp, mwp, mwp} , {mwp, mwp})
  • P = {project(money>money), work(money> money)}
    • p = ({mwp, mwp} , {mwp, mwp} , {mwp, mwp, mwp, mwp})
  • Symmetric merger:
    •  = ({mwp} , {mwp, mwp} , {mwp} , {mwp, mwp, mwp} , {mwp})

Lamsade DIMACS

application to qualitative decision example savage 54
Application to qualitative decisionExample (Savage\'54)
  • An agent is preparing an omelette.
  • 5 fresh eggs are already in the omelette.
  • There is one more egg.
  • The agent does not know whether this egg is fresh or rotten.
  • She can
    • add it to the omelette: the whole omelette may be wasted,
    • throw it away: one egg may be wasted, or
    • put it in a cup, check whether it is ok or not and add it to the omelette in the former case, throw it in the latter. A cup has to be washed.

Lamsade DIMACS

example savage 54 brewka 05
Example (Savage\'54, Brewka’05)
  • A controllable variable: in_omelette, in_cup, throw_away
  • An uncontrollable variable: fresh, rotten
  • Consequences of cont./uncont. variables:
    • 5_omelette  throw_away
    • 6_omelette  fresh, in_omelette
    • 0_omelette  rotten, in_omelette
    • 6_omelette  fresh, in_cup
    • 5_omelette  rotten, in_cup
    • wash  not in_cup
    • wash  in_cup
  • Agent\'s desires:
    • wash  wash
    • 6_omelette  5_omelette  0_omelette

Lamsade DIMACS

example savage 54 brewka 051
Example (Savage\'54, Brewka’05)
  • S1 = {6_omelette, wash, fresh, in_omelette}
  • S2 = {0_omelette, wash, rotten, in_omelette}
  • S3 = {6_omelette, wash, fresh, in_cup}
  • S4 = {5_omelette, wash, rotten, in_cup}
  • S5 = {5_omelette, wash, fresh, throw_away}
  • S6 = {5_omelette, wash, rotten, throw_away}

S1

S5 , S6

S3

Lamsade DIMACS

S2

S4

our approach extension of the example
Our approach: Extension of the example
  • Preferences over consequences + Preferences over alternatives

fresh  in_omelette > in_cup

fresh  in_cup > throw_away

rotten  throw_away > in_cup

rotten  in_cup > in_omelette

in_omelette  fresh > rotten

in_cup  fresh > rotten

throw_away  rotten > fresh

O =

P =

1: fresh  in_omelette, 2: rotten  in_omelette, 3: fresh  in_cup,

4: rotten  in_cup, 5: fresh  throw_away, 6: rotten  throw_away

  • o = ({1, 6} , {3, 4} , {2, 5})
  • p = ({1, 3, 6} , {2, 4, 5})
  • Symmetric merger:  = ({1, 6} , {3} , {4} , {2, 5})

Lamsade DIMACS

example2

S1

S5 , S6

S3

S2

S4

Example

1 , 6

  • S1 = {6_omelette, wash, fresh, in_omelette}
  • S2 = {0_omelette, wash, rotten, in_omelette}
  • S3 = {6_omelette, wash, fresh, in_cup}
  • S4 = {5_omelette, wash, rotten, in_cup}
  • S5 = {5_omelette, wash, fresh, throw_away}
  • S6 = {5_omelette, wash, rotten, throw_away}
    • wash  wash
    • 6_omelette  5_omelette  0_omelette

3

4

2 , 5

S1 > S6 > S3 > S4 > S5 > S2

Lamsade DIMACS

to summarize
To summarize

preferences on controllables

preferences on uncontrollables

o

p

pref. on contr./uncontr.

preferences

on consequences P

refine  with P

Lamsade DIMACS

another way

fresh  in_omelette > in_cup

fresh  in_cup > throw_away

rotten  throw_away > in_cup

rotten  in_cup > in_omelette

in_omelette  fresh > rotten

in_cup  fresh > rotten

throw_away  rotten > fresh

P =

O =

Another way
  • Preference statements involving consequence variables only
  • P = {wash > wash,

6_omelette > 5_omelette > 0_omelette,

5_omelette  wash > 0_omelette  wash}

  •  {in_omelettethrow_away > in_cup,

fresh(in_omelettein_cup) > throw_away(in_cuprotten),

throw_away(in_cuprotten) > rottenin_omelette,

in_cuprotten > in_omeletterotten}

Lamsade DIMACS

conclusion
Conclusion
  • non-monotonic logic of preferences + distinction between controllable and uncontrollable variables
  • Future research:
    • related works
    • more complex merging tasks: social and group decision making

Lamsade DIMACS

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