Compositional Creativity (ICFP 2017)

Transcript

1. ICFP 2017, Oxford, UK
   Compositional
   Creativity
   Chris Martens
   Assistant Professor
   Computer Science Department
   North Carolina State University
   

   View Slide

2. About Me
   Assistant Professor (UK equiv.: Lecturer) at NCSU
   Postdoc UC Santa Cruz, Expressive Intelligence Studio
   PhD CMU 2015, POP group
   2
   

   View Slide

3. About Me
   Conferences I used to
   go to had words like:
   functional, types,
   logic, deduction,
   languages
   3
   Conferences I go to
   now have words like:
   artificial intelligence,
   narrative, interactive
   storytelling, games,
   play
   

   View Slide

4. My Lab
   Conferences I used to
   go to had words like:
   functional, types,
   logic, deduction,
   languages
   4
   Conferences I go to
   now have words like:
   artificial intelligence,
   narrative, interactive
   storytelling, games,
   play
   

   View Slide

5. Research Mission
   Use principles from logic and
   formal methods to enable more
   expressive human-computer
   collaboration
   5
   

   View Slide

6. Human-Computer Collaboration
   ❖ Interactive storytelling
   ❖ Intelligent tutors
   ❖ Conversational agents
   ❖ Mixed-initiative creative tools
   6
   

   View Slide

7. “Artificial Intelligence”?
   ❖ Interactive storytelling
   ❖ Intelligent tutors
   ❖ Conversational agents
   ❖ Mixed-initiative creative tools
   7
   

   View Slide

8. Unifying themes: logic
   ❖ Logic as an intermediate
   language between human and
   computational thought
   ❖ Reasoning about synthesized
   behavior
   8
   

   View Slide

9. Unifying themes: social reasoning
   ❖ Simulating social agents
   ❖ Designing languages and other
   human-computer interfaces
   through a metaphor of
   conversation
   9
   

   View Slide

10. This talk
    From classical AI to modern FP
    Plots as plans as proofs
    Intentional reasoning
    Epistemic reasoning
    10
    

    View Slide

11. From classical AI to modern FP
    From classical AI to modern FP
    Plots as plans as proofs
    Intentional reasoning
    Epistemic reasoning
    11
    

    View Slide

12. A common origin of FP and AI, 1956
    12
    

    View Slide

13. Influence on AI
    First system to codify 

    reasoning as search
    Presented at McCarthy’s AI-defining Dartmouth Research Project, Summer 1956
    AI historian Pamela McCormick: “proof positive that a machine could perform
    tasks heretofore considered intelligent, creative and uniquely human”
    13
    

    View Slide

14. Influence on FP
    To build LTM, they implemented a new language called IPL
    Influenced McCarthy’s design of LISP
    Use of lists rather than arrays
    Hierarchical subroutines and recursion
    14
    

    View Slide

15. “Current Developments in
    Complex Information Processing”
    Allen Newell and Herbert Simon, 1959
    15
    

    View Slide

16. Reasoning as Search: 3 examples
    * Theorem proving
    * Program synthesis
    * AI planning
    16
    

    View Slide

17. Reasoning as Search: 3 examples
    * Theorem proving
    * Program synthesis
    * AI planning
    17
    

    View Slide

18. Theorem Proving
    Γ ⊢A
    18
    Initial
    Assumptions
    Goal
    Defined by atomic
    inference rules
    

    View Slide

19. Theorem Proving
    Γ ⊢A
    19
    Γ ⊢A
    Composition of inferences
    

    View Slide

20. Reasoning as Search: 3 examples
    * Theorem proving
    * Program synthesis
    * AI planning
    20
    

    View Slide

21. Reasoning as Search: 3 examples
    * Theorem proving
    * Program synthesis
    * AI planning
    21
    Conor McBride (since at least 2013):
    Type inference is so last century!
    Let’s write more detailed types, do program inference!
    

    View Slide

22. (Type-based) Program Synthesis
    Γ ⊢A
    22
    Library
    functions Specification
    Typing rules of the language
    

    View Slide

23. (Type-based) Program Synthesis
    Γ ⊢A
    :A
    let rec reverse l =
    case l of nil => …
    | cons x::xs => …
    Osera and Pierce - “Type-and-example-directed program
    synthesis,” POPL 2015;
    Polikarpova et al., “Program synthesis from polymorphic
    refinement types,” POPL 2016
    23
    Composition of program
    constructs
    

    View Slide

24. Reasoning as Search: 3 examples
    * Theorem proving
    * Program synthesis
    * AI planning
    24
    

    View Slide

25. AI Behavior Synthesis (Planning)
    Γ ⊢A
    25
    Initial State
    Goal state
    Atomic operators that can
    change the state
    

    View Slide

26. AI Behavior Synthesis (Planning)
    Γ ⊢A move a1 a2
    pickup block1
    move a2 b2
    place block1
    : { at(bot, a1), at(block1, a2)}
    —-> {at(bot, b2), at(block1, b2)}
    26
    Plan (sequence of operations)
    

    View Slide

27. Creative machines?
    * Theorem proving
    * Program synthesis
    * AI planning
    27
    

    View Slide

28. Plots as plans as proofs
    From classical AI to modern FP
    Plots as plans as proofs
    Intentional reasoning
    Epistemic reasoning
    28
    

    View Slide

29. AI Planning
    Domain - sets of operators (parameterized actions)
    Problem - initial and goal configuration
    —PLANNER—>
    plan, i.e.

    sequence of operators applied to terms to reach goal from initial
    29
    

    View Slide

30. AI Planning Domains
    PDDL/STRIPS - domain specific langs. for planners
    Actions defined in terms of of preconditions and effects
    Preconditions, effects, configurations, are collections of
    logical predicates
    30
    

    View Slide

31. Story Generation
    Planning for Plot Generation

    (Young 1999; Cavazza and Charles 2001-2)
    Linear Logic Programming for Plot Generation

    (Martens, Ferreira, Bosser, Cavazza 2013)
    31
    

    View Slide

32. Story Configurations
    initial: {
    dead(jon_arryn, hand),

    role(robert_baratheon, king),

    heir(robert_baratheon, joffrey),

    allies(robert_baratheon, eddard_stark),

    role(eddard_stark, warden_of_north)
    }
    sets of atomic propositions describing the world
    (Game-of-Thrones-inspired example)
    32
    ! "
    
    ❄
    
    
    
    (
    
    

    View Slide

33. Story Operators
    narrative events, e.g. ways characters can bid for power
    name_hand(Ruler, NewHand) :

    preconditions:
    need_filled(hand),

    role(Ruler, ruler_of_westeros),

    allies(Ruler, NewHand)
    effects:
    offered_role(NewHand, hand)

    delete need_filled(hand)
    33
    

    View Slide

34. Story Operators
    As a linear logic formula:
    name_hand(Ruler, NewHand) :
    need_filled(hand) *

    has_role(Ruler, ruler_of_westeros) *

    allies(Ruler, NewHand)
    -o
    offered_role(NewHand, hand) *

    has_role(Ruler, ruler_of_westeros) *

    allies(Ruler, NewHand)
    34
    

    View Slide

35. Compositional notation for plots
    35
    "
    
    !
    ❄
    
    
    " !
    (
    
    "
    

    View Slide

36. 36
    " names !
    "
    
    !
    ❄
    
    
    " !
    (
    
    "
    "
    
    
    " !
    !
    Compositional notation for plots
    

    View Slide

37. ! observes (
    37
    " names !
    "
    
    !
    ❄
    
    
    " !
    "
    
    
    " !
    (
    
    "
    ! …
    Compositional notation for plots
    

    View Slide

38. ! observes (
    38
    " names !
    "
    
    !
    ❄
    
    
    " !
    "
    
    
    " !
    (
    
    "
    ! …
    …
    …
    Compositional notation for plots
    

    View Slide

39. SEASON 1

    EPISODE 2
    39
    "
    
    !
    ❄
    
    
    " !
    (
    
    "
    …
    …
    …
    Compositional notation for plots
    

    View Slide

40. SEASON 1

    EPISODE 2
    40
    "
    
    !
    ❄
    
    
    " !
    (
    
    "
    …
    …
    …
    Compositional notation for plots
    c.f. symmetric monoidal categories
    

    View Slide

41. Story Generation
    goal: 

    has_role(!, )
    41
    Searching for plots with specified endings
    

    View Slide

42. Example: Story Generation
    Output: computer-generated fan fiction
    42
    

    View Slide

43. Narrative variation?
    goal: 

    Exists C. 

    has_role(C, ruler_of_westeros)
    43
    Searching for plots with varied endings
    

    View Slide

44. Planners & theorem provers find the most efficient solution
    

    

    : Exists C. has_role(C, ruler_of_westeros)
    44
    Narrative variation?
    

    View Slide

45. Planners & theorem provers find the most efficient solution
    has_role(rb, ruler_of_westeros) |- 

    

    : Exists C. has_role(C, ruler_of_westeros)
    45
    Narrative variation?
    

    View Slide

46. Planners & theorem provers find the most efficient solution
    has_role(rb, ruler_of_westeros) |- 

    

    “The end.”
    : Exists C. has_role(C, ruler_of_westeros)
    46
    Narrative variation?
    

    View Slide

47. Planners & theorem provers find the most efficient solution
    has_role(rb, ruler_of_westeros) |- 

    

    “The end.”
    : Exists C. has_role(C, ruler_of_westeros)
    Stories are anti-efficient!
    47
    Narrative variation?
    

    View Slide

48. A Partial Solution: Nondeterministic Proof Construction
    Linear logic for story generation: Martens et al. 2013 (LPNMR)
    Use forward chaining nondeterminism to leave goals unspecified,

    randomly explore the search space
    48
    Sacrifice completeness of search for variation in outcome
    

    View Slide

49. Another Limitation
    Stories generate interest e.g. through characters with conflicting goals
    Subterfuge, betrayal, suspense, etc. all depend on characters acting on goals with
    limited knowledge
    49
    

    View Slide

50. Meanwhile, in program synthesis…
    50
    

    View Slide

51. Adding constraints
    Program synthesis:

    Refining types with input-output examples (test cases)

    

    51
    f : int -> nat

    | f 1 => 1

    f 2 => 4

    f 5 => 25
    

    View Slide

52. Adding constraints
    Story generation:
    Enforcing intentional behavior in characters
    52
    

    View Slide

53. Intentional reasoning
    From classical AI to modern FP
    Plots as plans as proofs
    Intentional reasoning
    Epistemic reasoning
    53
    

    View Slide

54. Game AI: from opponents to cooperators
    Computer opponents (e.g. Chess, Go):

    moves need not be intelligible to human
    Computer cooperators:

    need to move in a legible, intentional-seeming way
    54
    

    View Slide

55. Grice's Maxims of Conversation
    ❖ Quantity - say neither too much nor too little
    ❖ Quality - tell the truth
    ❖ Relation - what is said should be relevant to
    the topic/stated intentions
    ❖ Manner - avoid obscurity and ambiguity
    55
    (Paul Grice, “Logic and Conversation,” 1975)
    

    View Slide

56. Hanabi
    Your hand is visible
    only to others
    Your shared goal is to
    build sequentially-
    ordered stacks of like-
    color cards
    56
    

    View Slide

57. Hanabi
    One turn:
    Play,
    Discard, or
    Give hint (spends a
    token)
    57
    

    View Slide

58. Hanabi: hints
    58
    

    View Slide

59. Computational cooperation in Hanabi
    ❖ Model the player’s knowledge, including their
    model of our knowledge
    ❖ Give hints to human players that will be
    recognized as intentional: point out cards when
    unambiguous whether to play or discard

    

    59
    

    View Slide

60. Computational cooperation in Hanabi
    ❖ Model the player’s knowledge, including their
    model of our knowledge
    ❖ Give hints to human players that will be
    recognized as intentional: point out cards when
    unambiguous whether to play or discard

    

    60
    }“Intentional”

    model
    

    View Slide

61. Computational cooperation in Hanabi
    ❖ Model the player’s knowledge, including their
    model of our knowledge
    ❖ Give hints to human players that will be
    recognized as intentional: point out cards when
    unambiguous whether to play or discard
    ❖ Interpret hints from human players as carrying the
    same intent; play or discard appropriately
    61
    }“Intentional”

    model
    {
    “Full”

    model
    

    View Slide

62. Computational Intelligence in Games (CIG) 2017
    3 implementations (base, intentional, full)
    +
    experimental evaluation
    1. Simulation of computer:computer
    2. Human subjects study, human:computer
    62
    

    View Slide

63. Computational Intelligence in Games (CIG) 2017
    63
    

    View Slide

64. Computational Intelligence in Games (CIG) 2017
    64
    Players rated more intentional agents both
    more enjoyable and more intentional-seeming
    

    View Slide

65. Grice's Maxims of Conversation
    Quantity - say neither too much nor too little
    ❖ Enforced by game rules
    65
    

    View Slide

66. Grice's Maxims of Conversation
    Quality - tell the truth
    ❖ Players have shared goals
    66
    

    View Slide

67. Grice's Maxims of Conversation
    Relation - be relevant
    ❖ Only give hints that can be
    interpreted as play/discard
    instructions
    67
    

    View Slide

68. Grice's Maxims of Conversation
    Manner - avoid ambiguity
    ❖ Only hint sets of cards for
    which the actionable subset is
    unambiguous
    68
    

    View Slide

69. Limitation
    Only one step of look-ahead
    How to apply intentional reasoning to search?
    69
    

    View Slide

70. Intentionality depends on Belief
    Transition from ad-hoc encoding of knowledge to formal
    Describe how beliefs influence actions and vice versa
    70
    

    View Slide

71. Epistemic reasoning
    From classical AI to modern FP
    Plots as plans as proofs
    Intentional reasoning
    Epistemic reasoning
    71
    

    View Slide

72. Theory of Mind
    Forming mental models of other
    people’s mental models
    72
    

    View Slide

73. Theory of Mind
    Forming mental models of other
    people’s mental models
    A key form of social reasoning in
    humans
    73
    

    View Slide

74. 3 Logicians Walk into a Pub
    74
    Will everyone
    have a beer?
    

    View Slide

75. 3 Logicians Walk into a Pub
    75
    Will everyone
    have a beer?
    I don’t know
    

    View Slide

76. 3 Logicians Walk into a Pub
    76
    Will everyone
    have a beer?
    I don’t knowI don’t know
    

    View Slide

77. 3 Logicians Walk into a Pub
    77
    Will everyone
    have a beer?
    I don’t knowI don’t know Yes!
    

    View Slide

78. Agent a believes A

    Epistemic Logic
    ☐a A

    78
    

    View Slide

79. Dynamic Epistemic Logic
    79
    ☐a A

    [α]A
    Agent a believes A

    A holds under action α
    

    View Slide

80. Agent a believes A

    A holds under action α
    Dynamic Epistemic Logic
    ☐a A

    [α]A
    80
    Actions may change the 

    actual world or the

    set of worlds an agent considers possible
    

    View Slide

81. Epistemic Actions (Baltag 2002)
    α, β ::= flip p 

    | ?A 

    | α + β 

    | α ; β 

    Change truth value

    Precondition

    Nondeterministic choice

    Sequence

    81
    

    View Slide

82. Epistemic Actions (Baltag 2002)
    α, β ::= flip p 

    | ?A 

    | α + β 

    | α ; β 

    | αa 

    | α*
    Change truth value

    Precondition

    Nondeterministic choice

    Sequence

    Appearance to a

    Public action
    82
    

    View Slide

83. Semantics: Possible Worlds
    Epistemic states:
    sets of world each agent considers possible
    83
    

    View Slide

84. Semantics: Possible Worlds
    An actual world
    84
    Set of world an agent considers

    possible
    

    View Slide

85. Semantics: Possible Worlds
    These sets can expand and contract based on actions
    85
    

    View Slide

86. Semantics: Possible Worlds
    86
    α
    Apply α
    

    View Slide

87. α
    α
    α
    α
    Semantics: Possible Worlds
    87
    α
    Apply α
    

    View Slide

88. Semantics: Possible Worlds
    88
    Apply α + β
    

    View Slide

89. Semantics: Possible Worlds
    89
    α
    Apply α + β
    β
    or
    α
    α
    α
    α
    β
    β
    β
    β
    

    View Slide

90. Semantics: Possible Worlds
    90
    Apply ?( v ); α
    

    View Slide

91. Semantics: Possible Worlds
    91
    α
    Apply ?( v ); α
    α α
    

    View Slide

92. –Petyr Baelish
    “Fight every battle everywhere, always, in your mind. Everyone is
    your enemy, everyone is your friend. Every possible series of events
    is happening all at once. Live that way and nothing will surprise
    you. Everything that happens will be something that you’ve seen
    before.”
    92
    

    View Slide

93. A tiny example
    Alice flips a coin in secret;

    Bob and Carol observe
    93
    coin(heads)Alice + coin(tails)Alice; 

    (coin(heads) + coin(tails)){Bob, Carol}
    

    View Slide

94. A practical action language?
    94
    Aggregate sums/products for expressing more than Boolean changes

    Term size blowup
    

    View Slide

95. Ostari - Eger & Martens 2017
    Parameterized actions

    Parameters can be secret to specific sets of agents
    95
    ⟨action⟩ ::= ⟨identifier⟩(⟨params⟩)
    

    View Slide

96. Ostari - Eger & Martens 2017
    ::=

    := 

    | learn 

    | public 

    | ;
    96
    ⟨action⟩ ::= ⟨identifier⟩(⟨params⟩)
    

    View Slide

97. Ostari - Eger & Martens 2017
    ::=

    := 

    | learn 

    | public 

    | ;
    97
    ⟨action⟩ ::= ⟨identifier⟩(⟨params⟩)
    

    View Slide

98. Ostari - Eger & Martens 2017
    ::=

    := 

    | learn 

    | public 

    | ;
    ::=

    exists x.

    | all x.

    | each x.

    | which x.
    98
    ⟨action⟩ ::= ⟨identifier⟩(⟨params⟩)
    

    View Slide

99. Ostari - Eger & Martens 2017
    ::=

    := 

    | learn 

    | public 

    | ;
    ::=

    exists x.

    | all x.

    | each x.

    | which x.
    99
    ⟨action⟩ ::= ⟨identifier⟩(⟨params⟩)
    

    View Slide

100. Epistemic Quantifiers
     100
     learn (p): exists c in Cards: at(deck, 1) == c.
     Useless knowledge
     

     View Slide

101. Epistemic Quantifiers
     101
     learn (p): which c in Cards: at(deck, 1) == c.
     Useful knowledge
     

     View Slide

102. Example
     102
     hintcolor(p: Players, c: Colors)
     learn (p): Each i in HandIndex:
     color(at(p, i)) == c
     Hinting a color in Hanabi
     

     View Slide

103. Implementation in Haskell

     (laziness useful for possible worlds representation!)
     Sequences of actions and queries
     Goals that generate action sequences
     Ostari - Eger & Martens 2017
     103
     

     View Slide

104. Epistemic Narrative Generation
     WorldA:

     at(Sherlock) = BakerStreet

     looks like (Sherlock): WorldA

     looks like (Moriarty): WorldA, WorldB
     WorldB:

     at(Sherlock) = ScotlandYard

     looks like (Sherlock): WorldB

     looks like (Moriarty): WorldA, WorldB
     104
     

     View Slide

105. Epistemic Narrative Generation
     goal: 

     murdered(Moriarty, Victim) ^

     ☐(Moriarty): ☐(Sherlock):
     exists M. 

     M != Moriarty ^ murdered(M, Victim)
     105
     

     View Slide

106. Epistemic Narrative Generation
     Generates a story in which Moriarty frames someone for murder
     goal: 

     murdered(Moriarty, Victim) ^

     ☐(Moriarty): ☐(Sherlock):
     exists M. 

     M != Moriarty ^ murdered(M, Victim)
     106
     

     View Slide

107. Summary
     3 investigations into using logic for creativity:
     1. Generating narrative with planning/linear logic
     2. Intentional reasoning in the context of cooperation
     3. Codifying intentionality with Epistemic Logic
     107
     

     View Slide

108. From modern FP to future AI
     From classical AI to modern FP
     Plots as plans as proofs
     Epistemic reasoning
     Intentional reasoning
     From modern FP to future AI
     108
     

     View Slide

109. Compositionality
     FP’s secret weapon
     [A ∘ B] == [A] [∘] [B]
     109
     

     View Slide

110. Compositionality
     110
     x f g z
     y y
     Function composition (meaning [-] is interface)
     

     View Slide

111. f ∘ g
     Compositionality
     Function composition (meaning [-] is interface)
     111
     x z
     

     View Slide

112. Compositionality
     Proof composition (use of lemmas)
     112
     
     C
     A
     ⊢
     Δ, ⊢
     A
     

     View Slide

113. Compositionality
     113
     ,
     C
     Δ
     ⊢
     Proof composition (use of lemmas)
     

     View Slide

114. Compositionality
     In planning: Frame Principle
     (“horizontal” composition)
     114
     Δ Δ’
     π
     ’
     ρ
     

     View Slide

115. Compositionality
     In planning: Frame Principle
     (“horizontal” composition)
     115
     Δ Δ’
     π

     ||

     ρ
     ’
     

     View Slide

116. Compositionality
     In planning linear logic: Frame Principle
     (“horizontal” composition)
     116
     Δ Δ’
     ’
     π

     ||

     ρ
     

     View Slide

117. Research Challenges
     Dynamic logics with functional action languages
     Constructive/lambda-calculable DEL
     Epistemic session types
     117
     

     View Slide

118. Compositional Creativity?
     asking computers to generate 

     insights, behaviors, narrative

     based on logical specifications
     118
     

     View Slide

119. Why Games and Stories?
     Logic is a great intermediate language
     between humans and machines, but
     insufficient
     Humans have been communicating through
     play and storytelling for even longer than
     they have been doing logic
     The best abstractions are discovered in
     diverse disciplines!
     119
     

     View Slide

120. Thanks!
     Chris Martens
     http://go.ncsu.edu/martens
     martens@csc.ncsu.edu
     @chrisamaphone
     github.com/chrisamaphone
     120
     

     View Slide