# The Wumpus World! 2012 级 ACM 班 金汶功. Hunt the wumpus!

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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

Reasoning via logic

Semantics

Models

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

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

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

Probabilistic Reasoning

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

Normalization

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

Full joint distribution

How likely is it that [1,3] has a pit?

Using independence

Simplification

Finally

Bayesian Network

Simple Example BurglaryEarthquake Alarm(Bark) John CallsMary Calls P(B).001 P(E).002 BEP(A) Truetrue.95 truefalse.94 falsetrue.29 false.001 BarkP(J) true.90 false.05 BarkP(M) true.70 false.01

Specification

Conditional Independence

Exact Inference

P1,3known b P3,1P2,2 P1,3P2,2P3,1b True 1 False1 TrueFalseTrue1 False 0 True 1 FalseTrueFalse1 True0 False 0 P(1,3) 0.2 P(known) P(P3,1) 0.2 P(P2,2) 0.2

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.

Reference http://zh.wikipedia.org/wiki/Hunt_the_Wumpus http://zh.wikipedia.org/wiki/%E8%B4%9D%E5%8F%B6%E6%9 6%AF%E7%BD%91%E7%BB%9C http://zh.wikipedia.org/wiki/%E8%B4%9D%E5%8F%B6%E6%9 6%AF%E7%BD%91%E7%BB%9C Stuart Russell, Peter Norvig Artificial Intelligence—A Modern Approach 3 rd edition, 2010

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