CS 380: ARTIFICIAL INTELLIGENCE LOGICAL AGENTS. Santiago Ontañón
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1 CS 380: RTIFICIL INTELLIGENCE LOGICL GENTS Santiago Ontañón
2 Summary so far: What is I? Rational gents Problem solving: Systematic search Uninformed search: DFS, BFS, ID Informed search: heuristics, Greedy Search, * Local Search: Hill Climbing, Simulated nnealing dversarial Search: Minima, alpha-beta, Monte Carlo Tree Search Net: knowledge representation + reasoning
3 Knowledge Knowledge base:
4 Knowledge Knowledge base: set of sentences in a formal language Knowledge-based agent: Inference engine Domain independent Knowledge base Domain specific Declarative programming
5 Declarative Programming Tell an agent WHT to do, but not HOW. Encode all the necessary knowledge, and let the agent infer how to achieve the goals. For eample, instead of programming quick sort, we would tell an agent: Here s a set of numbers. Now I want them sorted, which means that for every adjacent numbers, a, b, they must satisfy a <= b. You (the agent) figure out how J
6 Wumpus World PES description Performance measure gold +000, death per step, -0 for using the arrow Environment Squares adjacent to wumpus are smelly Squares adjacent to pit are breezy Glitter iff gold is in the same square Shooting kills wumpus if you are facing it Shooting uses up the only arrow Grabbing picks up gold if in same square Releasing drops the gold in same square ctuators Left turn, Right turn, Forward, Grab, Release, Shoot Sensors, Glitter, Smell 4 3 Stench Stench Gold Stench STRT 3 4 Chapter 7 5
7 Observable?? Wumpus world characterization Chapter 7 6
8 Wumpus world characterization Observable?? No only local perception Deterministic?? Chapter 7 7
9 Wumpus world characterization Observable?? No only local perception Deterministic?? Yes outcomes eactly specified Episodic?? Chapter 7 8
10 Wumpus world characterization Observable?? No only local perception Deterministic?? Yes outcomes eactly specified Episodic?? No sequential at the level of actions Static?? Chapter 7 9
11 Wumpus world characterization Observable?? No only local perception Deterministic?? Yes outcomes eactly specified Episodic?? No sequential at the level of actions Static?? Yes Wumpus and Pits do not move Discrete?? Chapter 7 0
12 Wumpus world characterization Observable?? No only local perception Deterministic?? Yes outcomes eactly specified Episodic?? No sequential at the level of actions Static?? Yes Wumpus and Pits do not move Discrete?? Yes Single-agent?? Chapter 7
13 Wumpus world characterization Observable?? No only local perception Deterministic?? Yes outcomes eactly specified Episodic?? No sequential at the level of actions Static?? Yes Wumpus and Pits do not move Discrete?? Yes Single-agent?? Yes Wumpus is essentially a natural feature Chapter 7
14 Eploring a wumpus world Chapter 7 3
15 Eploring a wumpus world B Chapter 7 4
16 Eploring a wumpus world B Chapter 7 5
17 Eploring a wumpus world B S Chapter 7 6
18 Eploring a wumpus world P B S W Chapter 7 7
19 Eploring a wumpus world P B S W Chapter 7 8
20 Eploring a wumpus world P B S W Chapter 7 9
21 Eploring a wumpus world P B BGS S W Chapter 7 0
22 Other tight spots B in (,) and (,) no safe actions B ssuming pits uniformly distributed, (,) has pit w/ prob 0.86, vs. 0.3 S Smell in (,) cannot move Can use a strategy of coercion: shoot straight ahead wumpus was there dead safe wumpus wasn t there safe Chapter 7
23 Logic in general Logics are formal languages for representing information such that conclusions can be drawn Synta defines the sentences in the language Semantics define the meaning of sentences; i.e., define truth of a sentence in a world E.g., the language of arithmetic + y is a sentence; + y > is not a sentence + y is true iff the number + is no less than the number y + y is true in a world where = 7, y = + y is false in a world where = 0, y = 6 Chapter 7
24 Entailment Entailment means that one thing follows from another: KB = α Knowledge base KB entails sentence α if and only if α is true in all worlds where KB is true E.g., the KB containing the Giants won and the Reds won entails Either the Giants won or the Reds won E.g., + y = 4 entails 4 = + y Entailment is a relationship between sentences (i.e., synta) that is based on semantics Note: brains process synta (of some sort) Chapter 7 3
25 Models Logicians typically think in terms of models, which are formally structured worlds with respect to which truth can be evaluated We say m is a model of a sentence α if α is true in m M(α) is the set of all models of α Then KB = α if and only if M(KB) M(α) E.g. KB = Giants won and Reds won α = Giants won M( ) M(KB) Chapter 7 4
26 Entailment in the wumpus world Situation after detecting nothing in [,], moving right, breeze in [,]?? Consider possible models for?s assuming only pits B? 3 Boolean choices 8 possible models Chapter 7 5
27 Wumpus models Chapter 7 6
28 Wumpus models KB KB = wumpus-world rules + observations Chapter 7 7
29 Wumpus models KB KB = wumpus-world rules + observations α = [,] is safe, KB = α, proved by model checking Chapter 7 8
30 Wumpus models KB KB = wumpus-world rules + observations Chapter 7 9
31 Wumpus models KB KB = wumpus-world rules + observations α = [,] is safe, KB = α Chapter 7 30
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