A simple knowledge-based agent function KB-Agent ( percept ) returns - PDF document

A simple knowledge-based agent function KB-Agent ( percept ) returns an action static : KB , a knowledge base t , a counter, initially 0, indicating time Logical agents Tell ( KB , Make-Percept-Sentence ( percept , t )) action ← Ask ( KB , Make-Action-Query ( t )) Tell ( KB , Make-Action-Sentence ( action , t )) t ← t + 1 return action Chapter 7 The agent must be able to: Represent states, actions, etc. Incorporate new percepts Update internal representations of the world Deduce hidden properties of the world Deduce appropriate actions Chapter 7 1 Chapter 7 4 Outline Wumpus World PEAS description ♦ Knowledge-based agents Performance measure gold +1000, death -1000 ♦ Wumpus world -1 per step, -10 for using the arrow Breeze Environment Stench 4 PIT ♦ Logic in general—models and entailment Squares adjacent to wumpus are smelly Breeze Breeze ♦ Propositional (Boolean) logic 3 PIT Squares adjacent to pit are breezy Stench Gold Glitter iff gold is in the same square ♦ Equivalence, validity, satisfiability Breeze Stench 2 Shooting kills wumpus if you are facing it ♦ Inference rules and theorem proving Shooting uses up the only arrow Breeze Breeze 1 PIT – forward chaining Grabbing picks up gold if in same square START Releasing drops the gold in same square – backward chaining 1 2 3 4 – resolution Actuators Left turn, Right turn, Forward, Grab, Release, Shoot Sensors Breeze, Glitter, Smell Chapter 7 2 Chapter 7 5 Knowledge bases Wumpus world characterization Inference engine domain−independent algorithms Observable?? Knowledge base domain−specific content Knowledge base = set of sentences in a formal language Declarative approach to building an agent (or other system): Tell it what it needs to know Then it can Ask itself what to do—answers should follow from the KB Agents can be viewed at the knowledge level i.e., what they know , regardless of how implemented Or at the implementation level i.e., data structures in KB and algorithms that manipulate them Chapter 7 3 Chapter 7 6

Wumpus world characterization Wumpus world characterization Observable?? No—only local perception Observable?? No—only local perception Deterministic?? Deterministic?? Yes—outcomes exactly specified Episodic?? No—sequential at the level of actions Static?? Yes—Wumpus and Pits do not move Discrete?? Chapter 7 7 Chapter 7 10 Wumpus world characterization Wumpus world characterization Observable?? No—only local perception Observable?? No—only local perception Deterministic?? Yes—outcomes exactly specified Deterministic?? Yes—outcomes exactly specified Episodic?? Episodic?? No—sequential at the level of actions Static?? Yes—Wumpus and Pits do not move Discrete?? Yes Single-agent?? Chapter 7 8 Chapter 7 11 Wumpus world characterization Wumpus world characterization Observable?? No—only local perception Observable?? No—only local perception Deterministic?? Yes—outcomes exactly specified Deterministic?? Yes—outcomes exactly specified Episodic?? No—sequential at the level of actions Episodic?? No—sequential at the level of actions Static?? Static?? Yes—Wumpus and Pits do not move Discrete?? Yes Single-agent?? Yes—Wumpus is essentially a natural feature Chapter 7 9 Chapter 7 12

Exploring a wumpus world Exploring a wumpus world P? OK B OK P? A S OK OK OK OK A A A Chapter 7 13 Chapter 7 16 Exploring a wumpus world Exploring a wumpus world P? P B OK B OK P? OK A A S OK OK OK OK W A A A Chapter 7 14 Chapter 7 17 Exploring a wumpus world Exploring a wumpus world P? P? P B OK P? B OK P? OK A A A S OK OK OK OK W A A A Chapter 7 15 Chapter 7 18

Exploring a wumpus world Logic in general Logics are formal languages for representing information such that conclusions can be drawn Syntax defines the sentences in the language Semantics define the “meaning” of sentences; P? OK P i.e., define truth of a sentence in a world E.g., the language of arithmetic B OK P? OK x + 2 ≥ y is a sentence; x 2 + y > is not a sentence OK A A x + 2 ≥ y is true iff the number x + 2 is no less than the number y S OK OK x + 2 ≥ y is true in a world where x = 7 , y = 1 W x + 2 ≥ y is false in a world where x = 0 , y = 6 A A Chapter 7 19 Chapter 7 22 Exploring a wumpus world Entailment Entailment means that one thing follows from another: KB | = α Knowledge base KB entails sentence α if and only if P? OK P 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” B OK P? BGS OK OK A A A E.g., x + y = 4 entails 4 = x + y Entailment is a relationship between sentences (i.e., syntax ) S OK OK W that is based on semantics A A Note: brains process syntax (of some sort) Chapter 7 20 Chapter 7 23 Other tight spots Models Logicians typically think in terms of models, which are formally P? structured worlds with respect to which truth can be evaluated Breeze in (1,2) and (2,1) We say m is a model of a sentence α if α is true in m B OK P? ⇒ no safe actions P? M ( α ) is the set of all models of α A Assuming pits uniformly distributed, Then KB | = α if and only if M ( KB ) ⊆ M ( α ) OK B OK x (2,2) has pit w/ prob 0.86, vs. 0.31 x x x P? A A x x E.g. KB = Giants won and Reds won x x x M( ) xx α = Giants won x x x x x x x x x x x x Smell in (1,1) x x x x x x xx x x x ⇒ cannot move x x x x x x Can use a strategy of coercion: M(KB) x x x x shoot straight ahead x x x S wumpus was there ⇒ dead ⇒ safe A wumpus wasn’t there ⇒ safe Chapter 7 21 Chapter 7 24

Entailment in the wumpus world Wumpus models 2 PIT 2 Breeze 1 Breeze 1 PIT 1 2 3 KB 1 2 3 Situation after detecting nothing in [1,1], 1 ? ? moving right, breeze in [2,1] PIT 2 PIT 2 2 Breeze 1 PIT Breeze 1 Breeze 1 ? 1 2 3 B 1 2 3 1 2 3 Consider possible models for ?s A A 2 PIT PIT assuming only pits 2 PIT Breeze 1 Breeze PIT 1 2 PIT PIT 3 Boolean choices ⇒ 8 possible models 1 2 3 1 2 3 Breeze PIT 1 1 2 3 KB = wumpus-world rules + observations α 1 = “[1,2] is safe”, KB | = α 1 , proved by model checking Chapter 7 25 Chapter 7 28 Wumpus models Wumpus models 2 PIT 2 PIT 2 2 Breeze Breeze 1 1 Breeze Breeze 1 PIT 1 PIT 1 2 3 1 2 3 KB 1 2 3 1 2 3 PIT PIT 2 2 PIT PIT 2 2 2 2 Breeze Breeze 1 PIT 1 PIT Breeze Breeze 1 1 Breeze Breeze 1 1 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 2 PIT PIT 2 PIT PIT 2 PIT 2 PIT Breeze Breeze 1 1 Breeze Breeze PIT PIT 1 1 2 PIT PIT 2 PIT PIT 1 2 3 1 2 3 1 2 3 1 2 3 Breeze Breeze PIT PIT 1 1 1 2 3 1 2 3 KB = wumpus-world rules + observations Chapter 7 26 Chapter 7 29 Wumpus models Wumpus models PIT 2 PIT 2 2 2 Breeze Breeze 1 1 2 Breeze Breeze 1 PIT 1 PIT 1 2 3 1 2 3 KB KB 1 2 3 1 2 3 2 PIT PIT 2 2 PIT PIT 2 2 2 Breeze PIT Breeze 1 1 PIT Breeze 1 Breeze 1 Breeze 1 Breeze 1 2 3 1 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 2 PIT PIT 2 PIT PIT PIT 2 2 PIT Breeze 1 Breeze Breeze 1 1 PIT Breeze 2 PIT PIT PIT 1 2 PIT PIT 1 2 3 1 2 3 1 2 3 1 2 3 Breeze PIT 1 Breeze PIT 1 1 2 3 1 2 3 KB = wumpus-world rules + observations KB = wumpus-world rules + observations α 2 = “[2,2] is safe”, KB �| = α 2 Chapter 7 27 Chapter 7 30