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The Wumpus World!

The Wumpus World!. 2012 级 ACM 班 金汶功. Hunt the wumpus !. Description. Performance measure Environment Actuators Sensors: Stench & Breeze & Glitter & Bump & Scream. An Example. An Example. Reasoning via logic. Semantics. Semantics: Relationship between logic and the real world

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The Wumpus World!

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  1. The Wumpus World! 2012级ACM班 金汶功

  2. Hunt the wumpus!

  3. Description • Performance measure • Environment • Actuators • Sensors: Stench & Breeze & Glitter & Bump & Scream

  4. An Example

  5. An Example

  6. Reasoning via logic

  7. Semantics • Semantics: Relationship between logic and the real world • Model: • Entailment:

  8. Models • KB: valid sentences • : “There is no pit in [1,2]” • : “There is no pit in [2,2]”

  9. Sensors Tell Knowledge base Axioms Agent Current States Ask Answer Tell Actuators Model checking

  10. Efficient Model Checking • DPLL • Early termination • Pure symbol heuristic • Unit clause heuristic • Component analysis • …

  11. Drawbacks • Model checking is NP-complete • Knowledge base may tell nothing.

  12. Probabilistic Reasoning

  13. Full joint probability distribution • P(X, Y) = P(X|Y)P(Y) • X: {1,2,3,4} -> {0.1,0.2,0.3,0.4} • Y: {a,b} -> {0.4, 0.6} • P(X = 2, Y = a) = P(X = 2|Y = a)P(Y = a) • The probability of all combination of values

  14. Normalization • is a constant

  15. The Wumpus World • Aim: calculate the probability that each of the three squares contains a pit.

  16. Full joint distribution • P(, ,,) P(,,|) P( • P( • Every room contains a pit of probability 0.2

  17. How likely is it that [1,3] has a pit? • Given observation: • terms

  18. Using independence

  19. Simplification • Now there are only 4 terms, cheers!

  20. Finally • [2,2] contains a pit with 86% probability! • Data structures---independence

  21. Bayesian Network

  22. Simple Example Burglary Earthquake Alarm(Bark) John Calls Mary Calls

  23. Specification • Each node corresponds to a random variable • Acyclic – DAG • Each node has a conditional probability distribution

  24. Conditional Independence

  25. Exact Inference

  26. P2,2 P3,1 P1,3 known b

  27. Approximate Inference • Markov Chain Monte Carlo • Gibbs Sampling • Idea: The long-run fraction of time spent in each state is exactly proportional to its posterior probability.

  28. Reference • http://zh.wikipedia.org/wiki/Hunt_the_Wumpus • http://zh.wikipedia.org/wiki/%E8%B4%9D%E5%8F%B6%E6%96%AF%E7%BD%91%E7%BB%9C • Stuart Russell, Peter NorvigArtificial Intelligence—A Modern Approach 3rd edition, 2010

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