Table of Contents Uncertainty Probability Syntax and Semantics Inference Independence and Bayes'Rule Bayesian network Graphical models Bayesian networks Inference in Bayesian networks 4口◆4⊙t1三1=，￥9QC
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table of Contents Uncertainty Probability Syntax and Semantics Inference Independence and Bayes’ Rule Bayesian network Graphical models Bayesian networks Inference in Bayesian networks
Syntax Basic element:random variable(随机变量)】 Similar to propositional logic:possible worlds defined by assignment of values to random variables. ,Boolean random variables(布尔随机变量) e.g,Cavity(牙洞)(do I have a cavity?) ,Discrete random variables(离散随机变量) e.g.,Weather is one of sunny,rainy,cloudy,snow Domain values must be exhaustive(穷尽的)and mutually exclusive（互斥的) Continuous random variables(连续随机变量) e.g.,Temp=21.6;also allow,e.g.,Temp 22.0 口卡回t·三4色，是分Q0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Syntax Basic element: random variable（随机变量） Similar to propositional logic: possible worlds defined by assignment of values to random variables. ▶ Boolean random variables（布尔随机变量） e.g., Cavity（牙洞）(do I have a cavity?) ▶ Discrete random variables（离散随机变量） e.g., Weather is one of ⟨ sunny, rainy, cloudy, snow ⟩ Domain values must be exhaustive（穷尽的）and mutually exclusive（互斥的） ▶ Continuous random variables（连续随机变量） e.g., Temp=21.6; also allow, e.g., Temp < 22.0
Syntax Elementary proposition (constructed by assignment of a value to a random variable: e.g.,Weather sunny,Cavity false (abbreviated as-cavity) Complex propositions formed from elementary propositions and standard logical connectives. e.g.,Weather sunny V Cavity false 4口◆4⊙t1三1=，￥9QC
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Syntax Elementary proposition（命题） constructed by assignment of a value to a random variable: e.g., Weather = sunny, Cavity = false (abbreviated as ¬ cavity) Complex propositions formed from elementary propositions and standard logical connectives. e.g., Weather = sunny ∨ Cavity = false
Syntax Atomic event:A complete specification of the state of the world about which the agent is uncertain 原子事件：对智能体无法确定的世界状态的一个完整的详细描 述。 e.g.,if the world consists of only two Boolean variables Cavity and Toothache,then there are 4 distinct atomic events: Cavity false A Toothache false Cavity false A Toothache true Cavity true A Toothache false Cavity true A Toothache true Atomic events are mutually exclusive(互斥)and exhaustive(穷尽 的) 口卡回t·三色，是分Q0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Syntax Atomic event: A complete specification of the state of the world about which the agent is uncertain 原子事件：对智能体无法确定的世界状态的一个完整的详细描 述。 e.g., if the world consists of only two Boolean variables Cavity and Toothache, then there are 4 distinct atomic events: ▶ Cavity = false ∧ Toothache = false ▶ Cavity = false ∧ Toothache = true ▶ Cavity = true ∧ Toothache = false ▶ Cavity = true ∧ Toothache = true Atomic events are mutually exclusive (互斥) and exhaustive（穷尽 的）
Axioms（公理)of probability For any propositions A,B ·0≤P(A≤1 P(true)=1 and P(false)=0 P(AVB)=P(A)+P(B)-P(AAB) True B 4口◆4⊙t1三1=，￥9QC
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Axioms（公理）of probability For any propositions A, B ▶ 0 ≤ P(A) ≤ 1 ▶ P(true) = 1 and P(false) = 0 ▶ P(A ∨ B) = P(A) + P(B) − P(A ∧ B)