asprin answer set programming with preferences
play

asprin : Answer Set Programming with Preferences Javier Romero - PowerPoint PPT Presentation

Sep 19, 2022 •351 likes •1.47k views

asprin : Answer Set Programming with Preferences Javier Romero University of Potsdam Javier Romero (KRR@UP) asprin : ASP with Preferences 1 / 55 Outline 1 Introduction 2 Declarative Problem Solving 3 An Example 4 Preliminaries 5 Language 6

  1. An Example Travelling Salesperson Problem class Find a route visiting every city once, and returning to the starting city { travel(X,Y) } :- road(X,Y,D). visited(Y) :- start(X), travel(X,Y). visited(Y) :- visited(X), travel(X,Y). :- city(X), not visited(X). :- city(X), 2 { travel(X,Y) }. Javier Romero (KRR@UP) asprin : ASP with Preferences 14 / 55

  2. An Example Travelling Salesperson Problem class Find a route visiting every city once, and returning to the starting city { travel(X,Y) } :- road(X,Y,D). visited(Y) :- start(X), travel(X,Y). visited(Y) :- visited(X), travel(X,Y). :- city(X), not visited(X). :- city(X), 2 { travel(X,Y) }. Javier Romero (KRR@UP) asprin : ASP with Preferences 14 / 55

  3. An Example Travelling Salesperson Problem class Find a route visiting every city once, and returning to the starting city { travel(X,Y) } :- road(X,Y,D). visited(Y) :- start(X), travel(X,Y). visited(Y) :- visited(X), travel(X,Y). :- city(X), not visited(X). :- city(X), 2 { travel(X,Y) }. Javier Romero (KRR@UP) asprin : ASP with Preferences 14 / 55

  4. An Example Travelling Salesperson Problem Solution ✻ Modeling Interpreting ❄ ✲ Logic Program Stable Models Solving Javier Romero (KRR@UP) asprin : ASP with Preferences 15 / 55

  5. An Example Travelling Salesperson $ clingo tsp.lp 0 clingo version 5.1.0 Reading from tsp.lp Solving... Answer: 1 travel(a,b) travel(b,c) travel(c,d) travel(d,a) ... Answer: 2 travel(a,b) travel(b,d) travel(d,c) travel(c,a) ... Answer: 3 travel(a,c) travel(c,b) travel(b,d) travel(d,a) ... SATISFIABLE Models : 3 Javier Romero (KRR@UP) asprin : ASP with Preferences 16 / 55

  6. An Example Travelling Salesperson $ clingo tsp.lp 0 clingo version 5.1.0 Reading from tsp.lp Solving... Answer: 1 travel(a,b) travel(b,c) travel(c,d) travel(d,a) ... Answer: 2 travel(a,b) travel(b,d) travel(d,c) travel(c,a) ... Answer: 3 travel(a,c) travel(c,b) travel(b,d) travel(d,a) ... SATISFIABLE Models : 3 Javier Romero (KRR@UP) asprin : ASP with Preferences 16 / 55

  7. An Example Travelling Salesperson Problem Solution ✻ Modeling Interpreting ❄ ✲ Logic Program Stable Models Solving Javier Romero (KRR@UP) asprin : ASP with Preferences 17 / 55

  8. An Example A route Answer: 1 travel(a,b) travel(b,c) travel(c,d) travel(d,a) ... Javier Romero (KRR@UP) asprin : ASP with Preferences 18 / 55

  9. An Example A route Answer: 1 travel(a,b) travel(b,c) travel(c,d) travel(d,a) ... 4 a b 3 3 4 c d Javier Romero (KRR@UP) asprin : ASP with Preferences 18 / 55

  10. An Example A route Answer: 2 travel(a,b) travel(b,d) travel(d,c) travel(c,a) ... 4 a b 5 5 4 c d Javier Romero (KRR@UP) asprin : ASP with Preferences 18 / 55

  11. An Example A route Answer: 3 travel(a,c) travel(c,b) travel(b,d) travel(d,a) ... a b 5 3 3 5 c d Javier Romero (KRR@UP) asprin : ASP with Preferences 18 / 55

  12. An Example asprin for Declarative Problem Solving Problem Solution ✻ Modeling Interpreting ❄ Logic Program ✲ Optimal with Preferences Stable Models Solving Javier Romero (KRR@UP) asprin : ASP with Preferences 19 / 55

  13. An Example asprin for Declarative Problem Solving Problem Solution ✻ Modeling Interpreting ❄ Logic Program Optimal ✲ with Preferences Stable Models Solving Javier Romero (KRR@UP) asprin : ASP with Preferences 19 / 55

  14. An Example Travelling Salesperson Problem class Find a route visiting every city once, and returning to the starting city. Prefer routes of minimum distance. 4 a b 5 3 3 5 4 c d Javier Romero (KRR@UP) asprin : ASP with Preferences 20 / 55

  15. An Example Travelling Salesperson Problem Solution ✻ Modeling Interpreting ❄ Logic Program Optimal ✲ Stable Models with Preferences Solving Javier Romero (KRR@UP) asprin : ASP with Preferences 21 / 55

  16. An Example Travelling Salesperson Problem class Find a route visiting every city once, and returning to the starting city. Prefer routes of minimum distance. #preference(distance,less(weight)){ D,(X,Y) :: travel(X,Y), road(X,Y,D) }. #optimize(distance). Javier Romero (KRR@UP) asprin : ASP with Preferences 22 / 55

  17. An Example Travelling Salesperson Problem class Find a route visiting every city once, and returning to the starting city. Prefer routes of minimum distance. #preference(distance,less(weight)){ D,(X,Y) :: travel(X,Y), road(X,Y,D) }. #optimize(distance). Javier Romero (KRR@UP) asprin : ASP with Preferences 22 / 55

  18. An Example Travelling Salesperson Problem class Find a route visiting every city once, and returning to the starting city. Prefer routes of minimum distance. #preference(distance,less(weight)){ D,(X,Y) :: travel(X,Y), road(X,Y,D) }. #optimize(distance). Javier Romero (KRR@UP) asprin : ASP with Preferences 22 / 55

  19. An Example Travelling Salesperson Problem Solution ✻ Modeling Interpreting ❄ Logic Program Optimal ✲ with Preferences Stable Models Solving Javier Romero (KRR@UP) asprin : ASP with Preferences 23 / 55

  20. An Example Travelling Salesperson $ asprin tsp.lp preference.lp 0 asprin version 3.0.0 Reading from tsp.lp ... Solving... Answer: 1 travel(a,c) travel(c,b) travel(b,d) travel(d,a) ... Answer: 2 travel(a,b) travel(b,c) travel(c,d) travel(d,a) ... OPTIMUM FOUND Models : 2 Optimum : yes Optimal : 1 Javier Romero (KRR@UP) asprin : ASP with Preferences 24 / 55

  21. An Example Travelling Salesperson $ asprin tsp.lp preference.lp 0 asprin version 3.0.0 Reading from tsp.lp ... Solving... Answer: 1 travel(a,c) travel(c,b) travel(b,d) travel(d,a) ... Answer: 2 travel(a,b) travel(b,c) travel(c,d) travel(d,a) ... OPTIMUM FOUND Models : 2 Optimum : yes Optimal : 1 Javier Romero (KRR@UP) asprin : ASP with Preferences 24 / 55

  22. An Example Travelling Salesperson Problem Solution ✻ Modeling Interpreting ❄ Logic Program Optimal ✲ with Preferences Stable Models Solving Javier Romero (KRR@UP) asprin : ASP with Preferences 25 / 55

  23. An Example A route Answer: 1 travel(a,c) travel(c,b) travel(b,d) travel(d,a) ... Answer: 2 travel(a,b) travel(b,c) travel(c,d) travel(d,a) ... OPTIMUM FOUND a b 5 3 3 5 c d Javier Romero (KRR@UP) asprin : ASP with Preferences 26 / 55

  24. An Example An optimal route Answer: 1 travel(a,c) travel(c,b) travel(b,d) travel(d,a) ... Answer: 2 travel(a,b) travel(b,c) travel(c,d) travel(d,a) ... OPTIMUM FOUND 4 a b 3 3 4 c d Javier Romero (KRR@UP) asprin : ASP with Preferences 26 / 55

  25. An Example Extending Travelling Salesperson Problem class Find a route visiting every city once, and returning to the starting city. Prefer going along the outside coast if it is cloudy, else prefer going through the inside mountains. type(X,Y,mountain) :- road(X,Y,D), D == 5. type(X,Y,coast) :- road(X,Y,D), D != 5. #preference(weather,aso){ travel(X,Y), type(X,Y,coast) >> travel(X’,Y), type(X’,Y,mountain) || cloudy; travel(X,Y), type(X,Y,mountain) >> travel(X’,Y), type(X’,Y,coast) || not cloudy }. #optimize(weather). Javier Romero (KRR@UP) asprin : ASP with Preferences 27 / 55

  26. An Example Extending Travelling Salesperson Problem class Find a route visiting every city once, and returning to the starting city. Prefer going along the outside coast if it is cloudy, else prefer going through the inside mountains. type(X,Y,mountain) :- road(X,Y,D), D == 5. type(X,Y,coast) :- road(X,Y,D), D != 5. #preference(weather,aso){ travel(X,Y), type(X,Y,coast) >> travel(X’,Y), type(X’,Y,mountain) || cloudy; travel(X,Y), type(X,Y,mountain) >> travel(X’,Y), type(X’,Y,coast) || not cloudy }. #optimize(weather). Javier Romero (KRR@UP) asprin : ASP with Preferences 27 / 55

  27. An Example Extending Travelling Salesperson Problem class Find a route visiting every city once, and returning to the starting city. Prefer going along the outside coast if it is cloudy, else prefer going through the inside mountains. type(X,Y,mountain) :- road(X,Y,D), D == 5. type(X,Y,coast) :- road(X,Y,D), D != 5. #preference(weather,aso){ travel(X,Y), type(X,Y,coast) >> travel(X’,Y), type(X’,Y,mountain) || cloudy; travel(X,Y), type(X,Y,mountain) >> travel(X’,Y), type(X’,Y,coast) || not cloudy }. #optimize(weather). Javier Romero (KRR@UP) asprin : ASP with Preferences 27 / 55

  28. An Example Extending Travelling Salesperson Problem class Find a route visiting every city once, and returning to the starting city. Prefer going along the outside coast if it is cloudy, else prefer going through the inside mountains. type(X,Y,mountain) :- road(X,Y,D), D == 5. type(X,Y,coast) :- road(X,Y,D), D != 5. #preference(weather,aso){ travel(X,Y), type(X,Y,coast) >> travel(X’,Y), type(X’,Y,mountain) || cloudy; travel(X,Y), type(X,Y,mountain) >> travel(X’,Y), type(X’,Y,coast) || not cloudy }. #optimize(weather). Javier Romero (KRR@UP) asprin : ASP with Preferences 27 / 55

  29. An Example Extending Travelling Salesperson $ asprin tsp.lp preference.lp 0 asprin version 3.0.0 Reading from tsp.lp ... Solving... Solving... Answer: 1 travel(a,b) travel(b,c) travel(c,d) travel(d,a) Answer: 2 travel(a,c) travel(b,d) travel(c,b) travel(d,a) OPTIMUM FOUND Answer: 3 travel(a,b) travel(b,d) travel(c,a) travel(d,c) OPTIMUM FOUND Models : 3 Optimum : yes Optimal : 2 Javier Romero (KRR@UP) asprin : ASP with Preferences 28 / 55

  30. An Example Extending Travelling Salesperson $ asprin tsp.lp preference.lp 0 asprin version 3.0.0 Reading from tsp.lp ... Solving... Solving... Answer: 1 travel(a,b) travel(b,c) travel(c,d) travel(d,a) Answer: 2 travel(a,c) travel(b,d) travel(c,b) travel(d,a) OPTIMUM FOUND Answer: 3 travel(a,b) travel(b,d) travel(c,a) travel(d,c) OPTIMUM FOUND Models : 3 Optimum : yes Optimal : 2 Javier Romero (KRR@UP) asprin : ASP with Preferences 28 / 55

  31. An Example Extending Travelling Salesperson Problem class Find a route visiting every city once, and returning to the starting city. Prefer routes of minimum distance. Prefer going through the outside coast if it is cloudy, else prefer going through the inside mountains. Combine both preferences with Pareto. #preference(all,pareto){ **distance; **weather }. #optimize(all). Javier Romero (KRR@UP) asprin : ASP with Preferences 29 / 55

  32. An Example Extending Travelling Salesperson Problem class Find a route visiting every city once, and returning to the starting city. Prefer routes of minimum distance. Prefer going through the outside coast if it is cloudy, else prefer going through the inside mountains. Combine both preferences with Pareto. #preference(all,pareto){ **distance; **weather }. #optimize(all). Javier Romero (KRR@UP) asprin : ASP with Preferences 29 / 55

  33. An Example Extending Travelling Salesperson $ asprin tsp.lp preference.lp 0 asprin version 3.0.0 Reading from tsp.lp ... Solving... Answer: 1 travel(a,b) travel(b,c) travel(c,d) travel(d,a) OPTIMUM FOUND Answer: 2 travel(a,c) travel(b,d) travel(c,b) travel(d,a) OPTIMUM FOUND Answer: 3 travel(a,b) travel(b,d) travel(c,a) travel(d,c) OPTIMUM FOUND Models : 3 Optimum : yes Optimal : 3 Javier Romero (KRR@UP) asprin : ASP with Preferences 30 / 55

  34. An Example Extending Travelling Salesperson $ asprin tsp.lp preference.lp 0 asprin version 3.0.0 Reading from tsp.lp ... Solving... Answer: 1 travel(a,b) travel(b,c) travel(c,d) travel(d,a) OPTIMUM FOUND Answer: 2 travel(a,c) travel(b,d) travel(c,b) travel(d,a) OPTIMUM FOUND Answer: 3 travel(a,b) travel(b,d) travel(c,a) travel(d,c) OPTIMUM FOUND Models : 3 Optimum : yes Optimal : 3 Javier Romero (KRR@UP) asprin : ASP with Preferences 30 / 55

  35. Preliminaries Outline 1 Introduction 2 Declarative Problem Solving 3 An Example 4 Preliminaries 5 Language 6 Implementation 7 Experimental analysis Boosting optimization via heuristics Dedicated systems versus asprin 8 Summary Javier Romero (KRR@UP) asprin : ASP with Preferences 31 / 55

  36. Preliminaries Preference A strict partial order ≻ on the stable models of a logic program That is, X ≻ Y means that X is preferred to Y A stable model X is ≻ -preferred, if there is no other stable model Y such that Y ≻ X A preference type is a (parametric) class of preference relations Example subset , pareto , etc. Javier Romero (KRR@UP) asprin : ASP with Preferences 32 / 55

  37. Preliminaries Preference A strict partial order ≻ on the stable models of a logic program That is, X ≻ Y means that X is preferred to Y A stable model X is ≻ -preferred, if there is no other stable model Y such that Y ≻ X A preference type is a (parametric) class of preference relations Example subset , pareto , etc. Javier Romero (KRR@UP) asprin : ASP with Preferences 32 / 55

  38. Preliminaries Preference A strict partial order ≻ on the stable models of a logic program That is, X ≻ Y means that X is preferred to Y A stable model X is ≻ -preferred, if there is no other stable model Y such that Y ≻ X A preference type is a (parametric) class of preference relations Example subset , pareto , etc. Javier Romero (KRR@UP) asprin : ASP with Preferences 32 / 55

  39. Language Outline 1 Introduction 2 Declarative Problem Solving 3 An Example 4 Preliminaries 5 Language 6 Implementation 7 Experimental analysis Boosting optimization via heuristics Dedicated systems versus asprin 8 Summary Javier Romero (KRR@UP) asprin : ASP with Preferences 33 / 55

  40. Language Language naming atom ∗∗ s where s is the name of a preference weighted formula w 1 , . . . , w l : φ where each w i is a term and φ is a Boolean formula preference element Φ 1 ≫ · · · ≫ Φ m � Φ m +1 where each Φ r is a set of weighted formulas preference statement # preference ( s , t ) { e 1 , . . . , e n } where s and t represent the preference statement and its type and each e j is a preference element optimization directive # optimize ( s ) where s is the name of a preference preference specification is a set S of preference statements and a directive # optimize ( s ) such that S is acyclic, closed, and s ∈ S Javier Romero (KRR@UP) asprin : ASP with Preferences 34 / 55

  41. Language Language naming atom ∗∗ s where s is the name of a preference weighted formula w 1 , . . . , w l : φ where each w i is a term and φ is a Boolean formula preference element Φ 1 ≫ · · · ≫ Φ m � Φ m +1 where each Φ r is a set of weighted formulas preference statement # preference ( s , t ) { e 1 , . . . , e n } where s and t represent the preference statement and its type and each e j is a preference element optimization directive # optimize ( s ) where s is the name of a preference preference specification is a set S of preference statements and a directive # optimize ( s ) such that S is acyclic, closed, and s ∈ S Javier Romero (KRR@UP) asprin : ASP with Preferences 34 / 55

  42. Language Language naming atom ∗∗ s where s is the name of a preference weighted formula w 1 , . . . , w l : φ where each w i is a term and φ is a Boolean formula preference element Φ 1 ≫ · · · ≫ Φ m � Φ m +1 where each Φ r is a set of weighted formulas preference statement # preference ( s , t ) { e 1 , . . . , e n } where s and t represent the preference statement and its type and each e j is a preference element optimization directive # optimize ( s ) where s is the name of a preference preference specification is a set S of preference statements and a directive # optimize ( s ) such that S is acyclic, closed, and s ∈ S Javier Romero (KRR@UP) asprin : ASP with Preferences 34 / 55

  43. Language Language naming atom ∗∗ s where s is the name of a preference weighted formula w 1 , . . . , w l : φ where each w i is a term and φ is a Boolean formula preference element Φ 1 ≫ · · · ≫ Φ m � Φ m +1 where each Φ r is a set of weighted formulas preference statement # preference ( s , t ) { e 1 , . . . , e n } where s and t represent the preference statement and its type and each e j is a preference element optimization directive # optimize ( s ) where s is the name of a preference preference specification is a set S of preference statements and a directive # optimize ( s ) such that S is acyclic, closed, and s ∈ S Javier Romero (KRR@UP) asprin : ASP with Preferences 34 / 55

  44. Language Language naming atom ∗∗ s where s is the name of a preference weighted formula w 1 , . . . , w l : φ where each w i is a term and φ is a Boolean formula preference element Φ 1 ≫ · · · ≫ Φ m � Φ m +1 where each Φ r is a set of weighted formulas preference statement # preference ( s , t ) { e 1 , . . . , e n } where s and t represent the preference statement and its type and each e j is a preference element optimization directive # optimize ( s ) where s is the name of a preference preference specification is a set S of preference statements and a directive # optimize ( s ) such that S is acyclic, closed, and s ∈ S Javier Romero (KRR@UP) asprin : ASP with Preferences 34 / 55

  45. Language Language naming atom ∗∗ s where s is the name of a preference weighted formula w 1 , . . . , w l : φ where each w i is a term and φ is a Boolean formula preference element Φ 1 ≫ · · · ≫ Φ m � Φ m +1 where each Φ r is a set of weighted formulas preference statement # preference ( s , t ) { e 1 , . . . , e n } where s and t represent the preference statement and its type and each e j is a preference element optimization directive # optimize ( s ) where s is the name of a preference preference specification is a set S of preference statements and a directive # optimize ( s ) such that S is acyclic, closed, and s ∈ S Javier Romero (KRR@UP) asprin : ASP with Preferences 34 / 55

  46. Language Language naming atom ∗∗ s where s is the name of a preference weighted formula w 1 , . . . , w l : φ where each w i is a term and φ is a Boolean formula preference element Φ 1 ≫ · · · ≫ Φ m � Φ m +1 where each Φ r is a set of weighted formulas preference statement # preference ( s , t ) { e 1 , . . . , e n } where s and t represent the preference statement and its type and each e j is a preference element optimization directive # optimize ( s ) where s is the name of a preference preference specification is a set S of preference statements and a directive # optimize ( s ) such that S is acyclic, closed, and s ∈ S Javier Romero (KRR@UP) asprin : ASP with Preferences 34 / 55

  47. Language Preference type A preference type t is a function mapping a set of preference elements E to a preference relation t ( E ) ⊆ A × A Examples ( X , Y ) ∈ subset ( E ) iff { ℓ ∈ E | X | = ℓ } ⊂ { ℓ ∈ E | Y | = ℓ } ( X , Y ) ∈ pareto ( E ) iff � ∗∗ s ∈ E ( X � s Y ) ∧ � ∗∗ s ∈ E ( X ≻ s Y ) Javier Romero (KRR@UP) asprin : ASP with Preferences 35 / 55

  48. Language Preference type A preference type t is a function mapping a set of preference elements E to a preference relation t ( E ) ⊆ A × A Examples ( X , Y ) ∈ subset ( E ) iff { ℓ ∈ E | X | = ℓ } ⊂ { ℓ ∈ E | Y | = ℓ } ( X , Y ) ∈ pareto ( E ) iff � ∗∗ s ∈ E ( X � s Y ) ∧ � ∗∗ s ∈ E ( X ≻ s Y ) Javier Romero (KRR@UP) asprin : ASP with Preferences 35 / 55

  49. Language Preference relation A preference relation is obtained by applying a preference type to a set of preference elements # preference ( s , t ) E declares preference relation t ( E ), denoted by ≻ s Example # preference (1 , subset ) { a , b , c } declares X ≻ 1 Y iff { ℓ ∈ { a , b , c } | X | = ℓ } ⊂ { ℓ ∈ { a , b , c } | Y | = ℓ } Javier Romero (KRR@UP) asprin : ASP with Preferences 36 / 55

  50. Language Preference relation A preference relation is obtained by applying a preference type to a set of preference elements # preference ( s , t ) E declares preference relation t ( E ), denoted by ≻ s Example # preference (1 , subset ) { a , b , c } declares X ≻ 1 Y iff { ℓ ∈ { a , b , c } | X | = ℓ } ⊂ { ℓ ∈ { a , b , c } | Y | = ℓ } Javier Romero (KRR@UP) asprin : ASP with Preferences 36 / 55

  51. Language Preference relation A preference relation is obtained by applying a preference type to a set of preference elements # preference ( s , t ) E declares preference relation t ( E ), denoted by ≻ s Example # preference (1 , subset ) { a , b , c } declares X ≻ 1 Y iff { ℓ ∈ { a , b , c } | X | = ℓ } ⊂ { ℓ ∈ { a , b , c } | Y | = ℓ } Javier Romero (KRR@UP) asprin : ASP with Preferences 36 / 55

  52. Implementation Outline 1 Introduction 2 Declarative Problem Solving 3 An Example 4 Preliminaries 5 Language 6 Implementation 7 Experimental analysis Boosting optimization via heuristics Dedicated systems versus asprin 8 Summary Javier Romero (KRR@UP) asprin : ASP with Preferences 37 / 55

  53. Implementation Preference program X = { holds ′ ( a ) | a ∈ X } Reification H X = { holds ( a ) | a ∈ X } and H ′ Preference program Let s be a preference statement declaring ≻ s . We define Q s as a preference program for s , if for all sets X , Y ⊆ A , we have iff Q s ∪ H X ∪ H ′ X ≻ s Y Y is satisfiable Note Q s is implemented as F s ∪ E t s ∪ C Note asprin ’s expressiveness is delineated by the decision problem Javier Romero (KRR@UP) asprin : ASP with Preferences 38 / 55

  54. Implementation Preference program X = { holds ′ ( a ) | a ∈ X } Reification H X = { holds ( a ) | a ∈ X } and H ′ Preference program Let s be a preference statement declaring ≻ s . We define Q s as a preference program for s , if for all sets X , Y ⊆ A , we have iff Q s ∪ H X ∪ H ′ X ≻ s Y Y is satisfiable Note Q s is implemented as F s ∪ E t s ∪ C Note asprin ’s expressiveness is delineated by the decision problem Javier Romero (KRR@UP) asprin : ASP with Preferences 38 / 55

  55. Implementation Preference program X = { holds ′ ( a ) | a ∈ X } Reification H X = { holds ( a ) | a ∈ X } and H ′ Preference program Let s be a preference statement declaring ≻ s . We define Q s as a preference program for s , if for all sets X , Y ⊆ A , we have iff Q s ∪ H X ∪ H ′ X ≻ s Y Y is satisfiable Note Q s is implemented as F s ∪ E t s ∪ C Note asprin ’s expressiveness is delineated by the decision problem Javier Romero (KRR@UP) asprin : ASP with Preferences 38 / 55

  56. Implementation Preference program X = { holds ′ ( a ) | a ∈ X } Reification H X = { holds ( a ) | a ∈ X } and H ′ Preference program Let s be a preference statement declaring ≻ s . We define Q s as a preference program for s , if for all sets X , Y ⊆ A , we have iff Q s ∪ H X ∪ H ′ X ≻ s Y Y is satisfiable Note Q s is implemented as F s ∪ E t s ∪ C Note asprin ’s expressiveness is delineated by the decision problem Javier Romero (KRR@UP) asprin : ASP with Preferences 38 / 55

  57. Implementation # preference (1 , subset ) { a , b , c } # optimize (1) � � H { a } = holds(a). H ′ � � { a , b } = holds ’(a). holds ’(b). � � preference (1, subset ). preference (1,1,1,for(a) ,()). = F 1 preference (1,2,1,for(b) ,()). optimize (1). preference (1,3,1,for(c) ,()). � � better(P) :- preference (P,subset), E subset = not holds(X), holds ’(X), preference(P,_,_,for(X),_), not holds(Y) : not holds ’(Y), preference(P,_,_,for(Y),_). � � C = :- optimize(P), not better(P). There is a stable model, indicating that { a } ≻ 1 { a , b } Javier Romero (KRR@UP) asprin : ASP with Preferences 39 / 55

  58. Implementation # preference (1 , subset ) { a , b , c } # optimize (1) � � H { a } = holds(a). H ′ � � { a , b } = holds ’(a). holds ’(b). � � preference (1, subset ). preference (1,1,1,for(a) ,()). = F 1 preference (1,2,1,for(b) ,()). optimize (1). preference (1,3,1,for(c) ,()). � � better(P) :- preference (P,subset), E subset = not holds(X), holds ’(X), preference(P,_,_,for(X),_), not holds(Y) : not holds ’(Y), preference(P,_,_,for(Y),_). � � C = :- optimize(P), not better(P). There is a stable model, indicating that { a } ≻ 1 { a , b } Javier Romero (KRR@UP) asprin : ASP with Preferences 39 / 55

  59. Implementation # preference (1 , subset ) { a , b , c } # optimize (1) � � H { a } = holds(a). H ′ � � { a , b } = holds ’(a). holds ’(b). � � preference (1, subset ). preference (1,1,1,for(a) ,()). = F 1 preference (1,2,1,for(b) ,()). optimize (1). preference (1,3,1,for(c) ,()). � � better(P) :- preference (P,subset), E subset = not holds(X), holds ’(X), preference(P,_,_,for(X),_), not holds(Y) : not holds ’(Y), preference(P,_,_,for(Y),_). � � C = :- optimize(P), not better(P). There is a stable model, indicating that { a } ≻ 1 { a , b } Javier Romero (KRR@UP) asprin : ASP with Preferences 39 / 55

  60. Implementation # preference (1 , subset ) { a , b , c } # optimize (1) � � H { a , b } = holds(a). holds(b). H ′ � � = holds ’(a). { a } � � preference (1, subset ). preference (1,1,1,for(a) ,()). = F 1 preference (1,2,1,for(b) ,()). optimize (1). preference (1,3,1,for(c) ,()). � � better(P) :- preference (P,subset), E subset = not holds(X), holds ’(X), preference(P,_,_,for(X),_), not holds(Y) : not holds ’(Y), preference(P,_,_,for(Y),_). � � C = :- optimize(P), not better(P). There is no stable model, indicating that { a , b } ⊁ 1 { a } Javier Romero (KRR@UP) asprin : ASP with Preferences 40 / 55

  61. Implementation Basic algorithm solveOpt ( P , s ) : A program P over A and preference statement s Input Output : A ≻ s -preferred stable model of P , if P is satisfiable, and ⊥ otherwise Y ← solve ( P ) if Y = ⊥ then return ⊥ repeat X ← Y P ∪ Q s ∪ R ∪ H ′ � � Y ← solve X until Y = ⊥ return X where R = { holds ( a ) ← a | a ∈ A} Javier Romero (KRR@UP) asprin : ASP with Preferences 41 / 55

  62. Implementation asprin ’s library Basic preference types subset and superset less(cardinality) and more(cardinality) less(weight) and more(weight) maxmin and minmax aso (Answer Set Optimization) poset (Qualitative Preferences) Composite preference types neg and pareto lexico And more to come. . . cp (restricted CP nets) Javier Romero (KRR@UP) asprin : ASP with Preferences 42 / 55

  63. Implementation asprin ’s library Basic preference types subset and superset less(cardinality) and more(cardinality) less(weight) and more(weight) maxmin and minmax aso (Answer Set Optimization) poset (Qualitative Preferences) Composite preference types neg and pareto lexico And more to come. . . cp (restricted CP nets) Javier Romero (KRR@UP) asprin : ASP with Preferences 42 / 55

  64. Experimental analysis Outline 1 Introduction 2 Declarative Problem Solving 3 An Example 4 Preliminaries 5 Language 6 Implementation 7 Experimental analysis Boosting optimization via heuristics Dedicated systems versus asprin 8 Summary Javier Romero (KRR@UP) asprin : ASP with Preferences 43 / 55

  65. Experimental analysis Boosting optimization via heuristics Outline 1 Introduction 2 Declarative Problem Solving 3 An Example 4 Preliminaries 5 Language 6 Implementation 7 Experimental analysis Boosting optimization via heuristics Dedicated systems versus asprin 8 Summary Javier Romero (KRR@UP) asprin : ASP with Preferences 44 / 55

  66. Experimental analysis Boosting optimization via heuristics Heuristic framework clingo allows for incorporating domain-specific heuristics into ASP solving input language for expressing domain-specific heuristics solving capacities for integrating domain-specific heuristics Heuristic directive #heuristic Heuristic modifiers (atom, a , and integer, v ) init for initializing the heuristic value of a with v factor for amplifying the heuristic value of a by factor v level for ranking all atoms; the rank of a is v sign for attributing the sign of v as truth value to a Heuristic statements #heuristic occurs(A,T) : action(A), time(T). [T,factor] Javier Romero (KRR@UP) asprin : ASP with Preferences 45 / 55

  67. Experimental analysis Boosting optimization via heuristics Heuristic framework clingo allows for incorporating domain-specific heuristics into ASP solving input language for expressing domain-specific heuristics solving capacities for integrating domain-specific heuristics Heuristic directive #heuristic Heuristic modifiers (atom, a , and integer, v ) init for initializing the heuristic value of a with v factor for amplifying the heuristic value of a by factor v level for ranking all atoms; the rank of a is v sign for attributing the sign of v as truth value to a Heuristic statements #heuristic occurs(A,T) : action(A), time(T). [T,factor] Javier Romero (KRR@UP) asprin : ASP with Preferences 45 / 55

  68. Experimental analysis Boosting optimization via heuristics Heuristic framework clingo allows for incorporating domain-specific heuristics into ASP solving input language for expressing domain-specific heuristics solving capacities for integrating domain-specific heuristics Heuristic directive #heuristic Heuristic modifiers (atom, a , and integer, v ) init for initializing the heuristic value of a with v factor for amplifying the heuristic value of a by factor v level for ranking all atoms; the rank of a is v sign for attributing the sign of v as truth value to a Heuristic statements #heuristic occurs(A,T) : action(A), time(T). [T,factor] Javier Romero (KRR@UP) asprin : ASP with Preferences 45 / 55

  69. Experimental analysis Boosting optimization via heuristics Heuristic framework clingo allows for incorporating domain-specific heuristics into ASP solving input language for expressing domain-specific heuristics solving capacities for integrating domain-specific heuristics Heuristic directive #heuristic Heuristic modifiers (atom, a , and integer, v ) init for initializing the heuristic value of a with v factor for amplifying the heuristic value of a by factor v level for ranking all atoms; the rank of a is v sign for attributing the sign of v as truth value to a Heuristic statements #heuristic occurs(A,T) : action(A), time(T). [T,factor] Javier Romero (KRR@UP) asprin : ASP with Preferences 45 / 55

  70. Experimental analysis Boosting optimization via heuristics Heuristic framework clingo allows for incorporating domain-specific heuristics into ASP solving input language for expressing domain-specific heuristics solving capacities for integrating domain-specific heuristics Heuristic directive #heuristic Heuristic modifiers (atom, a , and integer, v ) init for initializing the heuristic value of a with v factor for amplifying the heuristic value of a by factor v level for ranking all atoms; the rank of a is v sign for attributing the sign of v as truth value to a Heuristic statements #heuristic occurs(mv,5) : action(mv), time(5). [5,factor] Javier Romero (KRR@UP) asprin : ASP with Preferences 45 / 55

  71. Experimental analysis Boosting optimization via heuristics asprin with different heuristic settings Benchmark \ System asprin asprin w + s asprin w + l asprin w + f asprin asprin s + s asprin s + l asprin s + f w s Ricochet (30) 20.00 432 ( 8, 4) 407 ( 7, 4) 68 ( 1, 0) 71 (1, 0) 365 ( 8, 3) 461 ( 7, 10) 69 (1, 0) 71 (1, 0) Timetabling (12) 23687.75 345 (285, 3) 255 (202, 2) 900 ( 4, 12) 6 (1, 0) 217 (144, 2) 21 (18, 0) 900 (2, 12) 5 (1, 0) Puzzle (7) 580.57 82 ( 2, 0) 112 ( 2, 0) 136 ( 2, 0) 416 (2, 1) 31 ( 1, 0) 32 ( 1, 0) 21 (1, 0) 51 (1, 0) Crossing (24) 211.92 104 ( 42, 1) 98 ( 35, 0) 805 (19, 20) 387 (6, 6) 0 ( 6, 0) 1 ( 6, 0) 7 (9, 0) 3 (1, 0) Valves (30) 56.63 69 ( 7, 0) 65 ( 6, 0) 460 ( 8, 11) 715 (0, 22) 38 ( 4, 0) 39 ( 4, 0) 339 (4, 6) 673 (0, 21) Expansion (30) 7501.87 216 (299, 0) 10 ( 15, 0) 38 ( 7, 0) 12 (3, 0) 64 (295, 0) 14 (54, 0) 4 (4, 0) 3 (1, 0) Repair (30) 6750.73 76 ( 48, 0) 15 ( 47, 0) 71 ( 3, 2) 8 (2, 0) 8 ( 43, 0) 3 (11, 0) 1 (1, 0) 1 (1, 0) Diagnosis (30) 1669.00 196 (341, 3) 76 ( 66, 0) 43 ( 4, 0) 118 (3, 2) 19 (338, 0) 2 (39, 0) 0 (1, 0) 0 (1, 0) ∅ ( ∅ , Σ) 190 (129, 11) 130 ( 48, 6) 315 ( 6, 45) 217 (2, 31) 93 (105, 5) 72 (18, 10) 168 (3, 18) 101 (1, 21) asprin w asprin s asprin w + s asprin s + s asprin w + l asprin s + l asprin w + f asprin s + f w — weight-based s — subset-based s — sign heuristic s — sign heuristic l — level-based heuristic l — level-based heuristic f — factor-based heuristic f — factor-based heuristic Javier Romero (KRR@UP) asprin : ASP with Preferences 46 / 55

  72. Experimental analysis Boosting optimization via heuristics asprin with different heuristic settings Benchmark \ System asprin asprin w + s asprin w + l asprin w + f asprin asprin s + s asprin s + l asprin s + f w s Ricochet (30) 20.00 432 ( 8, 4) 407 ( 7, 4) 68 ( 1, 0) 71 (1, 0) 365 ( 8, 3) 461 ( 7, 10) 69 (1, 0) 71 (1, 0) Timetabling (12) 23687.75 345 (285, 3) 255 (202, 2) 900 ( 4, 12) 6 (1, 0) 217 (144, 2) 21 (18, 0) 900 (2, 12) 5 (1, 0) Puzzle (7) 580.57 82 ( 2, 0) 112 ( 2, 0) 136 ( 2, 0) 416 (2, 1) 31 ( 1, 0) 32 ( 1, 0) 21 (1, 0) 51 (1, 0) Crossing (24) 211.92 104 ( 42, 1) 98 ( 35, 0) 805 (19, 20) 387 (6, 6) 0 ( 6, 0) 1 ( 6, 0) 7 (9, 0) 3 (1, 0) Valves (30) 56.63 69 ( 7, 0) 65 ( 6, 0) 460 ( 8, 11) 715 (0, 22) 38 ( 4, 0) 39 ( 4, 0) 339 (4, 6) 673 (0, 21) Expansion (30) 7501.87 216 (299, 0) 10 ( 15, 0) 38 ( 7, 0) 12 (3, 0) 64 (295, 0) 14 (54, 0) 4 (4, 0) 3 (1, 0) Repair (30) 6750.73 76 ( 48, 0) 15 ( 47, 0) 71 ( 3, 2) 8 (2, 0) 8 ( 43, 0) 3 (11, 0) 1 (1, 0) 1 (1, 0) Diagnosis (30) 1669.00 196 (341, 3) 76 ( 66, 0) 43 ( 4, 0) 118 (3, 2) 19 (338, 0) 2 (39, 0) 0 (1, 0) 0 (1, 0) ∅ ( ∅ , Σ) 190 (129, 11) 130 ( 48, 6) 315 ( 6, 45) 217 (2, 31) 93 (105, 5) 72 (18, 10) 168 (3, 18) 101 (1, 21) asprin w asprin s asprin w + s asprin s + s asprin w + l asprin s + l asprin w + f asprin s + f w — weight-based s — subset-based s — sign heuristic s — sign heuristic l — level-based heuristic l — level-based heuristic f — factor-based heuristic f — factor-based heuristic Javier Romero (KRR@UP) asprin : ASP with Preferences 47 / 55

  73. Experimental analysis Boosting optimization via heuristics asprin with different heuristic settings Benchmark \ System asprin asprin w + s asprin w + l asprin w + f asprin asprin s + s asprin s + l asprin s + f w s Ricochet (30) 20.00 432 ( 8, 4) 407 ( 7, 4) 68 ( 1, 0) 71 (1, 0) 365 ( 8, 3) 461 ( 7, 10) 69 (1, 0) 71 (1, 0) Timetabling (12) 23687.75 345 (285, 3) 255 (202, 2) 900 ( 4, 12) 6 (1, 0) 217 (144, 2) 21 (18, 0) 900 (2, 12) 5 (1, 0) Puzzle (7) 580.57 82 ( 2, 0) 112 ( 2, 0) 136 ( 2, 0) 416 (2, 1) 31 ( 1, 0) 32 ( 1, 0) 21 (1, 0) 51 (1, 0) Crossing (24) 211.92 104 ( 42, 1) 98 ( 35, 0) 805 (19, 20) 387 (6, 6) 0 ( 6, 0) 1 ( 6, 0) 7 (9, 0) 3 (1, 0) Valves (30) 56.63 69 ( 7, 0) 65 ( 6, 0) 460 ( 8, 11) 715 (0, 22) 38 ( 4, 0) 39 ( 4, 0) 339 (4, 6) 673 (0, 21) Expansion (30) 7501.87 216 (299, 0) 10 ( 15, 0) 38 ( 7, 0) 12 (3, 0) 64 (295, 0) 14 (54, 0) 4 (4, 0) 3 (1, 0) Repair (30) 6750.73 76 ( 48, 0) 15 ( 47, 0) 71 ( 3, 2) 8 (2, 0) 8 ( 43, 0) 3 (11, 0) 1 (1, 0) 1 (1, 0) Diagnosis (30) 1669.00 196 (341, 3) 76 ( 66, 0) 43 ( 4, 0) 118 (3, 2) 19 (338, 0) 2 (39, 0) 0 (1, 0) 0 (1, 0) ∅ ( ∅ , Σ) 190 (129, 11) 130 ( 48, 6) 315 ( 6, 45) 217 (2, 31) 93 (105, 5) 72 (18, 10) 168 (3, 18) 101 (1, 21) asprin w asprin s asprin w + s asprin s + s asprin w + l asprin s + l asprin w + f asprin s + f w — weight-based s — subset-based s — sign heuristic s — sign heuristic l — level-based heuristic l — level-based heuristic f — factor-based heuristic f — factor-based heuristic Javier Romero (KRR@UP) asprin : ASP with Preferences 48 / 55

Recommend

Using Answer Set Programming for Representating and Reasoning about Preferences and Uncertainty

Using Answer Set Programming for Representating and Reasoning about Preferences and Uncertainty

Using Answer Set Programming for Representating and Reasoning about Preferences and Uncertainty in Dynamic Domains Ravi Palla 1 , 2 , Dan Tecuci 1 , Vinay Shet 1 , Mathaeus Dejori 1 1 Siemens Corporate Research, Princeton, NJ, USA 2 School of

664 views • 32 slides
The Joy of Probabilistic Answer Set Programming Fabio G. Cozman Universidade de S ao Paulo

The Joy of Probabilistic Answer Set Programming Fabio G. Cozman Universidade de S ao Paulo

The Joy of Probabilistic Answer Set Programming Fabio G. Cozman Universidade de S ao Paulo Goal: to show that the credal semantics for Probabilistic Answer Set Programming (PASP) leads to a very useful modeling language. Answer set

375 views • 14 slides
Knowledge Representation for the Semantic Web Lecture 7: Answer Set Programming II Daria

Knowledge Representation for the Semantic Web Lecture 7: Answer Set Programming II Daria

More about Logic Programs ASP Paradigm Programming Techniques Answer Set Solvers Knowledge Representation for the Semantic Web Lecture 7: Answer Set Programming II Daria Stepanova partially based on slides by Thomas Eiter D5: Databases and

1.04k views • 89 slides
Table of Contents I Answer Set Programming ASP Solvers Example: Hamiltonian Cycles Choice Rules

Table of Contents I Answer Set Programming ASP Solvers Example: Hamiltonian Cycles Choice Rules

Table of Contents I Answer Set Programming ASP Solvers Example: Hamiltonian Cycles Choice Rules Solving Puzzles Yulia Kahl College of Charleston Artificial Intelligence 1 Reading Read Chapter 6, Answer-Set Programming Paradigm , in the

199 views • 15 slides
Approximated Probabilistic Answer Set Programming Eduardo Menezes de Morais Department of

Approximated Probabilistic Answer Set Programming Eduardo Menezes de Morais Department of

Motivation ASP PSAT Probabilistic Answer Set Programming Resolution Methods Approximations Future work Approximated Probabilistic Answer Set Programming Eduardo Menezes de Morais Department of Computer Science Universidade de S ao

808 views • 48 slides
Knowledge Representation for the Semantic Web Lecture 6: Answer Set Programming I Daria Stepanova

Knowledge Representation for the Semantic Web Lecture 6: Answer Set Programming I Daria Stepanova

Introduction Horn Logic Programming Negation in Logic Programs Answer Set Semantics Knowledge Representation for the Semantic Web Lecture 6: Answer Set Programming I Daria Stepanova partially based on slides by Thomas Eiter D5: Databases and

1.28k views • 82 slides
Towards Programming Support Methods for Answer-Set Programs Hans Tompits Vienna University of

Towards Programming Support Methods for Answer-Set Programs Hans Tompits Vienna University of

Towards Programming Support Methods for Answer-Set Programs Hans Tompits Vienna University of Technology Institute of Information Systems Knowledge-Based Systems Group Context: Answer-Set Programming ( ASP ) Important paradigm for

490 views • 23 slides
Moral Preferences F R A N C E S C A R O S S I Decision making Based on our preferences

Moral Preferences F R A N C E S C A R O S S I Decision making Based on our preferences

Moral Preferences F R A N C E S C A R O S S I Decision making Based on our preferences over the options Social context: aggregation of the individuals preferences Voting rules: from collection of preference orderings to a

485 views • 19 slides
Answer Set Programming in a Nutshell Torsten Schaub University of Potsdam Torsten Schaub

Answer Set Programming in a Nutshell Torsten Schaub University of Potsdam Torsten Schaub

Answer Set Programming in a Nutshell Torsten Schaub University of Potsdam Torsten Schaub (KRR@UP) Answer Set Programming in a Nutshell 1 / 31 Outline 1 Introduction 2 Foundations 3 Modeling 4 Algorithms and Systems 5 Potassco 6 Summary

1.07k views • 86 slides
Enhancing Efficiency and Expressiveness in Answer Set Programming Systems Wolfgang Faber

Enhancing Efficiency and Expressiveness in Answer Set Programming Systems Wolfgang Faber

0 Enhancing Efficiency and Expressiveness in Answer Set Programming Systems Wolfgang Faber faber@kr.tuwien.ac.at Enhancing Efficiency and Expressiveness in ASP Systems 1 Agenda Answer Set Programming Syntax and Semantics Answer

424 views • 23 slides
Outline Motivation Answer Set Programming is a well-known declarative problem solving approach.

Outline Motivation Answer Set Programming is a well-known declarative problem solving approach.

Motivation Motivation Outline Motivation Answer Set Programming is a well-known declarative problem solving approach. Answer Set Programs with Queries over Subprograms 1 Motivation Christoph Redl The Saturation Technique and its

259 views • 10 slides
Answer Set Programming, the Solving Paradigm for Knowledge Representation and Reasoning Martin

Answer Set Programming, the Solving Paradigm for Knowledge Representation and Reasoning Martin

Answer Set Programming, the Solving Paradigm for Knowledge Representation and Reasoning Martin Gebser Torsten Schaub University of Potsdam Martin Gebser (University of Potsdam) Answer Set Programming 1 / 33 Outline 1 Motivation 2

1.36k views • 105 slides
Knowledge Representation for the Semantic Web Lecture 8: Answer Set Programming III Daria

Knowledge Representation for the Semantic Web Lecture 8: Answer Set Programming III Daria

The DLV System and its Features Weak Constraints Aggregates DLV Usage: Examples Overview: DLV -Extensions Knowledge Representation for the Semantic Web Lecture 8: Answer Set Programming III Daria Stepanova partially based on slides by Thomas

1.07k views • 103 slides
Knowledge Representation for the Semantic Web Lecture 8: Answer Set Programming III Daria

Knowledge Representation for the Semantic Web Lecture 8: Answer Set Programming III Daria

DLs vs ASP DL-programs Other ASP Extensions Rule Learning Knowledge Representation for the Semantic Web Lecture 8: Answer Set Programming III Daria Stepanova D5: Databases and Information Systems Max Planck Institute for Informatics WS

1.66k views • 76 slides
The 6th Answer Set Programming Competition Martin Gebser, Marco Maratea, Francesco Ricca 13th

The 6th Answer Set Programming Competition Martin Gebser, Marco Maratea, Francesco Ricca 13th

The Sixth ASP Competition Format and Setup Participants and Results The 6th Answer Set Programming Competition Martin Gebser, Marco Maratea, Francesco Ricca 13th International Conference on Logic Programming and Non-monotonic Reasoning 1/66

967 views • 75 slides
Constraint Answer Set Programming without Grounding J. Arias 1 , 2 M. Carro 1 , 2 E. Salazar 3 K.

Constraint Answer Set Programming without Grounding J. Arias 1 , 2 M. Carro 1 , 2 E. Salazar 3 K.

Jul 14, 2018 [ICLP-2018] Constraint Answer Set Programming without Grounding J. Arias 1 , 2 M. Carro 1 , 2 E. Salazar 3 K. Marple 3 G. Gupta 3 1 IMDEA Software Institute, 2 Universidad Polit ecnica de Madrid, 3 University of Texas at Dallas

778 views • 75 slides
A Framework for Easing the Development of Applications Embedding Answer Set Programming Davide

A Framework for Easing the Development of Applications Embedding Answer Set Programming Davide

A Framework for Easing the Development of Applications Embedding Answer Set Programming Davide Fusc Stefano Germano Jessica Zangari Marco Anastasio Francesco Calimeri Simona Perri 18th International Symposium on Principles and Practice

1.18k views • 81 slides
A Framework for Easing the Development of Applications Embedding Answer Set Programming* Davide

A Framework for Easing the Development of Applications Embedding Answer Set Programming* Davide

A Framework for Easing the Development of Applications Embedding Answer Set Programming* Davide Fusc Stefano Germano Jessica Zangari Marco Anastasio Francesco Calimeri Simona Perri 23rd RCRA International Workshop on Experimental

886 views • 70 slides
Answer Set Programming and Human-Robot Interactions: Challenges and Opportunities Tran Cao Son

Answer Set Programming and Human-Robot Interactions: Challenges and Opportunities Tran Cao Son

Answer Set Programming and Human-Robot Interactions: Challenges and Opportunities Tran Cao Son Computer Science, New Mexico State University, Las Cruces, NM (Joint work with: Chitta Baral, Michael Gelfond, and Arindam Mitra) Dresden 2016 Tran

755 views • 44 slides
Axiomatic Foundations of Multiplier Preferences Tomasz Strzalecki Multiplier preferences

Axiomatic Foundations of Multiplier Preferences Tomasz Strzalecki Multiplier preferences

Axiomatic Foundations of Multiplier Preferences Tomasz Strzalecki Multiplier preferences Expected Utility inconsistent with observed behavior We (economists) may not want to fully trust any probabilistic model. Hansen and Sargent:

879 views • 84 slides
Parsing Combinatory Categorial Grammar with Answer Set Programming: Preliminary Report Yuliya

Parsing Combinatory Categorial Grammar with Answer Set Programming: Preliminary Report Yuliya

Parsing Combinatory Categorial Grammar with Answer Set Programming: Preliminary Report Yuliya Lierler Peter Schller Computer Science Department, University of Kentucky KBS Group Institut fr Informationssysteme, Technische Universitt

548 views • 26 slides
Modeling and Reasoning in Event Calculus Using Goal-Directed Constraint Answer Set Programming n

Modeling and Reasoning in Event Calculus Using Goal-Directed Constraint Answer Set Programming n

9 Oct, 2019 [LOPSTR19] Modeling and Reasoning in Event Calculus Using Goal-Directed Constraint Answer Set Programming n Arias 1 , 2 Zhuo Chen 3 Manuel Carro 1 , 2 Gopal Gupta 3 Joaqu 1 IMDEA Software Institute, 2 Universidad Polit ecnica

524 views • 39 slides
Rational preferences Idea: preferences of a rational agent must obey constraints. Rational

Rational preferences Idea: preferences of a rational agent must obey constraints. Rational

Rational preferences Idea: preferences of a rational agent must obey constraints. Rational preferences behavior describable as maximization of expected utility Rational decisions Constraints: Orderability ( A B ) ( B A ) (

197 views • 4 slides
Rational preferences Idea: preferences of a rational agent must obey constraints. Rational

Rational preferences Idea: preferences of a rational agent must obey constraints. Rational

Rational preferences Idea: preferences of a rational agent must obey constraints. Rational preferences behavior describable as maximization of expected utility Rational decisions Constraints: Orderability ( A B ) ( B A ) (

320 views • 5 slides

More recommend