Reasoning About Actions, Events, and Beliefs

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Reasoning About Actions, Events, and Beliefs
R N 10.3
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When Theres More than One Reality

• John is a person.
• John is an artist.
• John is wearing a black hat.
• John entered the room.
• Mary knows that John entered the room.
• Mary knows that someone came in.
• Mary doesnt know that John entered the room.

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Reasoning about Change
A situation is a possible world in which a set of
facts is true. Winnie is a bear. He is in the
park carrying his camera. He walked home.
Bear(Winnie, s0) Inpark(Winnie,
s0) Holding(Winnie, Camera1, s0) Ownerof(Camera1,
Winnie, s0) Home(Winnie, s1)
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Reasoning about Change
Winnie is a bear. He is in the park carrying his
camera. He walked home. One the way, he lost
his camera. Bear(Winnie, s0) Inpark(Winnie,
s0) Holding(Winnie, Camera1, s0) Ownerof(Camera1,
Winnie, s0) Home(Winnie, s2)
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Axiomatizing Change (and Stasis)
Give(Pooh, Piglet, Cherries) true if Pooh gave
Piglet cherries Precondition ?x, y, z, s0
Have(x, z, s0) ? Possible(Give(x, y, z,
s0)) Postcondition Give(x, y, z, s0) ?
Have(y, z, Result(Give(x, y, z, s0)))
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Axiomatizing Change (and Stasis)
Give(Pooh, Piglet, Cherries) an object
corresponding to an event Precondition
?x, y, z, s0 Have(x, z, s0) ? Possible(Give(x, y,
z, s0)) Postcondition Possible(Give(x, y, z,
s0))? Have(y, z, Result(Give(x, y, z, s0)))
Possible(Give(x, y, z, s0))? Have(y, z,
next-situation(Give(x, y, z, s0))) Result (or
next-situation) is a function that returns a new
situation.
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Asserting that an Event Happened
KM (new-situation) (_situation1) KM (have Pooh
Cherries) KM (a giving with (agent
Pooh) (object Cherries) (recipient
Piglet)) (_giving6) KM (do-and-next _giving6)
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Whats True in a New Situation?

• Winnie is a bear. He is in the park carrying his
  camera. He walked home.
• Bear(Winnie, s0)
• Inpark(Winnie, s0)
• Holding(Winnie, Camera1, s0)
• Ownerof(Camera1, Winnie, s0)
• Fluents - change with the situation
• Inertial fluents - can change but persist unless
  told otherwise
• Non-fluents - dont change from one situation to
  the next (also called atemporal or eternal
  predicates)

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The Frame Problem

• Inferring things that stay the same
• Frame axioms
• ?x, y, s0 Have(x, y, s0) ? Have(x, y,
  Result(Go(x, p)))
• The issues
• Representing the facts concisely
• Inferring the facts efficiently
• What if there are rare situations that interfere
  with the standard inferences?

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Reasoning About Beliefs

• Representing propositional attitudes
• An analog of the frame problem the complexity of
  managing belief spaces
• Referential transparency

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Representing Propositional Attitudes
Believes(Winnie, Has(Piglet, honey)) Problem?
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Representing Propositional Attitudes
Believes(Winnie, Has(Piglet, honey)) Problem? So
lution Modal logics
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Managing Belief Spaces
Believes(Winnie, Has(Piglet, honey)) Believes(Pigl
et, Has(Piglet, honey)) Enter Eeyeore What does
Eeyore believe?
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How Far Does It Go?
She knew I knew she knew I knew she knew.
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Referential Transparency
?x car(x) ? owns(Jan, x) car(s1) ? owns(Jan,
s1) ?x car(x) ? indriveway(x) car(s2) ?
indriveway(x2) color(x2, red) x1 x2 ? ?x
car(x) ? owns(Jan, x) ? color(x, red) But now
what happens if were reasoning about
belief Jimmy knew that Santa Claus left the
stockings. Mom Santa Claus Did Jimmy know that
Mom left the stockings?