CHAPTER 7. LOGICAL AGENT

Inha University

Intelligent E-Commerce Systems Lab

CHAPTER 7.

LOGICAL AGENT

석사 1 차 지 애 띠


OUTLINE

KNOWLEDGE-BASED AGENTS

THE WUMPUS WORLD

LOGIC

PROPOSITIONAL LOGIC

AGENT BASED ON PROPOSITIONAL LOGIC


KNOWLEDGE-BASED AGENTS

Knowledge Base - a set of representations of facts about the

world - a set of sentences that is expressed in a knowledge representation language

Knowledge-Based Agent deriving new

sentence from old one

Knowledge base

Inference engine


KNOWLEDGE-BASED AGENTS Outline of a knowledge-Based Agent

First, it TELLs the KB what it perceives (a way to add new sentences to the KB) Second, it ASKs the KB what action it should perform (a way to query what is known)

function KB-AGENT(percept) returns an action static: KB, a knowledge base t, a counter, initially 0, indicating time

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


THE WUMPUS WORLD Performance measure Environment Actuators – turn left, turn right, die, forward, grab, shoot Sensors

the agent will perceive a stench in the square containing the wumpus and the directly adjacent squares

the agent will perceive a breeze in the squares directly adjacent to a pit

the agent will perceive a glitter in the square where the gold is

the agent will perceive a bump when it walks into a wall the agent will perceive a scream anywhere in the cave when t

he wumpus is killed.


THE WUMPUS WORLD

B = Breeze

G = Glitter, Gold

OK = Safe square

P = Pit

S = Stench

V = Visited

W = Wumpus

A = Agent


THE WUMPUS WORLD

1, 4

1, 3

1, 2

1, 1

2, 4

2, 3

2, 2

2, 1

3, 4

3, 3

3, 2

3, 1

4, 4

4, 3

4, 2

4, 1

B = Breeze

G = Glitter, Gold

OK = Safe square

P = Pit

S = Stench

V = Visited

W = Wumpus

A = Agent

AOK OK

OK

V B

P?

P?P!

OKS

W!

V

S G V

V

P?

P?

V


LOGIC

Logic

formal language for provided the syntax and semantics are defined precisely

Syntax - the sentences in the language ex) x y

Semantics - the “meaning” of sentences ex) x y is false when y is bigger than x,

and true otherwise Model – possible world


LOGIC

KB : “KB entails ”KB entails sentence if and only if is true in all worlds

where KB is true

KB : “ is derived from KB by i” or “i derives from KB”

Soundness i is sound if whenever KB , it is also true that KB

Completeness i is complete if whenever KB , it is also true that KB

i

i

i


PROPOSITIONAL LOGIC : Semantics Truth Table

Equivalence, Validity, & Satisfiability Two sentences are equivalence if they are true in the s

ame set of models A sentence is valid if it it true in all models A sentence is satisfiable if it is true in some model A sentence is unsatisfiable if it is true in no models

P QFalse False

TrueFalseFalseTrue

True True

ㄱ P P Q∧ P Q∨ P Q⇒ P⇔Q

FalseFalse

FalseFalseFalse

False

False FalseFalse

TrueTrue

True

TrueTrueTrue True True

TrueTrueTrue


PROPOSITIONAL LOGIC : Inference Modus Ponens (=Implication-Elimination)

And-Elimination

Double-Negation Elimination

Unit Resolution

Resolution

α β, α ⇒β

α1 α2 α3 ... αn ∧ ∧ ∧ ∧αi

ㄱㄱ α α

α β, ∨ ㄱ β α

α β, ∨ ㄱ β∨γ α γ∨

ㄱ α β, β γ ⇒ ⇒ㄱ α γ⇒=


AGENT BASED ON PROPOSITIONAL LOGIC Current state

ㄱ S1,1 ㄱ S2,1 S1,2

ㄱ B1,1 B2,1 ㄱ B1,2

Rules R1 ㄱ S1,1⇒ ㄱ W1,1∧ ㄱ W1,2∧ ㄱ W2,1

R2 ㄱ S2,1⇒ ㄱ W1,1∧ ㄱ W2,1∧ ㄱ W2,2∧ ㄱ W3,1

R3 S1,2⇒ W1,3∨W1,2∨W2,2∨W1,1

2,1 B V OK

1,1 V OK

1,2 A S OK

1,3 W!

1,4

2,2 OK

2,3

2,4

3,1 P!

3,2

3,3

3,4

4,1

4,2

4,3

4,4


AGENT BASED ON PROPOSITIONAL LOGIC 1. Modus Ponens & And-Elimination : ㄱ S1,1 & R1 ㄱ W1,1 ㄱ W1,2 ㄱ W2,1 2. Modus Ponens & And-Elimination : ㄱ S2,1 & R2 ㄱ W2,2 ㄱ W2,1 ㄱ W3,1 3. Modus Ponens : S1,2 & R4 W1,3∨W1,2∨W2,2∨W1,1 4. Unit Resolution α : W1,3∨W1,2∨W2,2 β : W1,1 ( ㄱ W1,1 from 1) W1,3∨W1,2∨W2,2 5. Unit Resolution α : W1,3∨W1,2∨W2,2 β : W2,2 ( ㄱ W2,2 from 2) W1,3∨W1,2 6. nit Resolution α : W1,3∨W1,2 β : W1,2 ( ㄱ W1,2 from 2) W1,3


AGENT BASED ON PROPOSITIONAL LOGIC Finding pits and wumpuses using logical inference

A knowledge base that states the “physics” of the wumpus world : ㄱ P1,1 and ㄱ W1,1

Bx,y ⇔ (Px,y+1 ∨ Px,y-1 ∨ Px+1,y ∨ Px-1,y) Sx,y ⇔ (Wx,y+1 ∨ Wx,y-1 ∨ Wx+1,y ∨ Wx-1,y) W1,1 ∨ W1,2 ∨ … ∨ W4,3 ∨ W4,4 - at least one To say that there in at most one wumpus, we needs a total of

155 sentences containing 64 distinct symbols

Keeping track of location and orientation Lx,y ∧ FacingRightt ∧ Forwardt ⇒ Lt+1

x+1,y Propositions need to depend on time If a agent moves 100 steps, it needs 6400 rules


SUMMARY

Propositional Logic Syntax : formal structure of sentences Semantics : truth of sentences Validity & Inference

Problems of propositional logic In First-order logic, 6400 propositional rules

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CHAPTER 7. LOGICAL AGENT

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