Reasoning about controllable and uncontrollable variables
This presentation is the property of its rightful owner.
Sponsored Links
1 / 23

Reasoning about controllable and uncontrollable variables PowerPoint PPT Presentation


  • 91 Views
  • Uploaded on
  • Presentation posted in: General

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

Download Presentation

Reasoning about controllable and uncontrollable variables

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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


  • Login