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Reasoning About Actions, Events, and Beliefs

Reasoning About Actions, Events, and Beliefs. R & N 10.3. When There’s 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.

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Reasoning About Actions, Events, and Beliefs

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  1. Reasoning About Actions, Events, and Beliefs R & N 10.3

  2. When There’s 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 doesn’t know that John entered the room.

  3. 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)

  4. 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)

  5. 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)))

  6. 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.

  7. 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)

  8. What’s 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 - don’t change from one situation to the next (also called atemporal or eternal predicates)

  9. 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?

  10. Reasoning About Beliefs • Representing propositional attitudes • An analog of the frame problem: the complexity of managing belief spaces • Referential transparency

  11. Representing Propositional Attitudes • Believes(Winnie, Has(Piglet, honey)) • Problem?

  12. Representing Propositional Attitudes • Believes(Winnie, Has(Piglet, honey)) • Problem? • Solution: Modal logics

  13. Managing Belief Spaces • Believes(Winnie, Has(Piglet, honey)) • Believes(Piglet, Has(Piglet, honey)) • Enter Eeyeore • What does Eeyore believe?

  14. How Far Does It Go? “She knew I knew she knew I knew she knew.”

  15. 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 we’re reasoning about belief: Jimmy knew that Santa Claus left the stockings. Mom = Santa Claus Did Jimmy know that Mom left the stockings?

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