Reasoning About Actions, Events, and Beliefs: Reasoning About Actions, Events, and Beliefs R andamp; N 10.3


When There’s More than One Reality: 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.


Reasoning about Change: 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)


Reasoning about Change: 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)


Axiomatizing Change (and Stasis) : 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)))


Axiomatizing Change (and Stasis) : 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.


Asserting that an Event Happened: Asserting that an Event Happened KMandgt; (new-situation) (_situation1) KMandgt; (have Pooh Cherries) KMandgt; (a giving with (agent Pooh) (object Cherries) (recipient Piglet)) (_giving6) KMandgt; (do-and-next _giving6)


What’s True in a New Situation?: 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)


The Frame Problem: 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?


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


Representing Propositional Attitudes: Representing Propositional Attitudes Believes(Winnie, Has(Piglet, honey)) Problem?


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


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


How Far Does It Go?: How Far Does It Go? 'She knew I knew she knew I knew she knew.'


Referential Transparency: 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?