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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. Preference reasoning. Logics of preferences attract much attention in KR Application: qualitative decision making

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Reasoning about controllable and uncontrollable variables

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  1. Reasoning about controllable and uncontrollable variables Souhila KACI CRIL-CNRS Lens Leendert van der Torre ILIAS Luxembourg Lamsade DIMACS

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. Contr./Uncontr. variables & Qualitative decision theory • states, actions, consequences • state variables: • observable variables  controllable variables • unobservable variables  uncontrollable variables • actions: controllable variables Lamsade DIMACS

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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. To summarize preferences on controllables preferences on uncontrollables o p  pref. on contr./uncontr. preferences on consequences P refine  with P Lamsade DIMACS

  22. 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

  23. 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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