1

UNIT-3

KNOWLEDGE REPRESENTATION

2

Agents that reason logically(Logical agents)

• A Knowledge based Agent• The Wumpus world environment• Representation, Reasoning and Logic• Logics – An Introduction• Propositional Logic• An Agent for the wumpus world –

Propositional Logic

3

Abilities KB agent

• Agent must be able to:• Represent states and actions,• Incorporate new percepts• Update internal representation of the

world• Deduce hidden properties of the world• Deduce appropriate actions

4

Agents that Reason Logically

• Logical agents have knowledge base, from which they draw conclusions• TELL: provide new facts to agent• ASK: decide on appropriate action

5

Sample: Wumpus World

• Show original wumpus game• goal is to shoot wumpus• example of logical reasoning

• Our version:• Find gold, avoid wumpus, climb back

out of cave

6

A Wumpus Agent

• Agent does not perceive its own location (unlike sample game), but it can keep track of where it has been

• Percepts:• Stench – wumpus is nearby• Breeze – pit is nearby• Glitter – gold is here• Bump – agent has just bumped against a

wall• Scream – agent has heard another player die

7

Wumpus Agent

• Actuators:• Forward, Turn Left, Turn Right• Grab (gold)• Shoot (shoots arrow forward until hits

wumpus or wall)•agent only has one arrow

• Climb (exit the cave)• Environment:

• 4x4 grid, start at (1,1) facing right

8

Wumpus Agent

• Death• Agent dies if it enters a pit or square

with wumpus• Goal: get gold and climb back out. Don’t

die.• 1000 points for climbing out of cave

with gold• 1 point penalty for each action taken• 10,000 point penalty for death

9

Some complex reasoning examples

• Start in (1,1)• Breeze in (1,2) and (2,1)• Probably a pit in (2,2)

• Smell in (1,1) – where can you go?• Pick a direction – shoot• Walk in that direction• Know where wumpus is

10

Another example solution

No perception 1,2 and 2,1 OK

Move to 2,1

B in 2,1 2,2 or 3,1 P?

1,1 V no P in 1,1

Move to 1,2 (only option)

11

Example solution

S and No S when in 2,1 1,3 or 1,2 has W

1,2 OK 1,3 W

No B in 1,2 2,2 OK & 3,1 P

12

AI Models and Propositional Logic

•The Role of a Model•Represent The Environment•Assimilate Knowledge•Learning•Simulation•Inference

13

Models

• If we are going to create programs that are intelligent, then we need to figure out how to represent models

• They allow us to predict certain things about the future.

14

The Role of a Model

• Represent the environment

• Provide a structure for the assimilation of new knowledge

15

Represent The Environment

• Features in the environment must be represented as features in the model

• They should be able to act in the model just as they do in the environment

• Needs to be able to represent both long term qualities of the environment and short term states.

16

Assimilate Knowledge

• A model of the world allows an agent to organize new information in the context of what it already knows and draw conclusions.

17

Learning

• An AI agent may start ready programmed with knowledge, or it may have to learn it from experience

• The model may change in response to new experiences.

18

Simulation

• Simulate the real environment to test potential actions.

• The model needs to accept simulated sensory input and it needs to feed simulated actions back in without actually making those actions in reality

• It needs an imagination

19

Inference

• Inference is the process of deriving a conclusion based on what is known

20

Representation, Reasoning and logic

21

Logic in general

22

Ontological and Epistemological Assumptions

• ontological assumption :It is understood in connection to the logic of functioning of the agent.

- question is: “What does the agent do?” This means discussing both what the agent is and what its behavior constitutes of.

• Epistemological assumptions: It consider the nature of knowledge.

- question is: “On what knowledge does the agent base its actions?” It is important to discuss the origins of knowledge as well as concepts such as learning and memory.

23

Types of logic

24

The use of logic

• A logic: formal language for representing information, rules for drawing conclusions

• Two kinds of logics:• Propositional Logic

• Represents facts

• First Order Logic • Represents facts, objects, and relations

RQP

)()( xMammalxCatx

25

Entailment

• One thing follows from anotherKB |= (knowledge base entails alpha)

• KB entails sentence if and only if is true in worlds where KB is true.

g. x+y=4 entails 4=x+y

• Entailment is a relationship between sentences that is based on semantics.

26

Propositional Logic

• Represents facts as being either true or false• Formally represented by a letter, e.g. P or Q.• Actually refer to facts about the environment, e.g.

the speed limit in town is 30mph• Single facts can be combined into sentences using

Boolean operators• These sentences, if true, can become facts in the KB.• A KB is said to entail a sentence if it is true in the

KB

27

Logic consists of

• Logical constants: true, false• Proposition symbols: P, Q, R, ...• Logical connectives: & (or ^), , ¬, →, ↔ • Parentheses: ( )• Propositional logic is an extremely simple

representation

28

Basic symbols

• Expressions only evaluate to either “true” or “false.”

• P “P is true”• ¬P “P is false” negation• P V Q “either P is true or Q is true or both” disjunction• P ^ Q “both P and Q are true” conjunction• P => Q “if P is true, the Q is true” implication• P Q “P and Q are either both true or both false”

equivalence

29

For example

30

Syntax rules for propositional logic

• The constants true and false are propositions by themselves.

• A proposition symbol such as P or Q is a proposition by itself.

• Wrapping parentheses around a proposition produces proposition.

31

Ambiguity

The grammar can be ambiguous, for example: P & Q R.

It is best to use parentheses to eliminate ambiguity. When ambiguity is present, we resolve it with

operator precedence:(highest) : ¬ ,& , ,, (lowest) For example: ¬P Q & R ) Sis equivalent to: ((¬ P) (Q & R)) S

32

Limitations of Propositional Logic

1. It is too weak, i.e., has very limited expressiveness:• Each rule has to be represented for each situation:

e.g., “don’t go forward if the wumpus is in front of you” takes 64 rules

2. It cannot keep track of changes:• If one needs to track changes, e.g., where the agent has been

before then we need a timed-version of each rule. To track 100 steps we’ll then need 6400 rules for the previous example.

Its hard to write and maintain such a huge rule-baseInference becomes intractable

33

Inference rules

34

An Agent for the wumpus world – Propositional Logic

35

Example of using logic in Wumpus World

StenchAgent

Start Breeze

• KB contains:

2,2

2,1

1,2

1,1

S

S

S

S

2,2

2,1

1,2

1,1

B

B

B

B

36

KB also contains knowledge of environment

• No stench no wumpus nearby

• Stench wumpus nearby

3,12,22,11,12,13

1,32,21,21,11,22

1,22,11,11,11

:

:

:

WWWWSR

WWWWSR

WWWSR

3,12,22,11,12,14 : WWWWSR

37

We can determine where wumpus is!

• Method 1: Truth table• At least 14 symbols currently: S1,1, S2,1,

S1,2, S2,2, W1,1, W2,1, W1,2, W2,2, W3,1, W1,3, B1,1, B2,1, B1,2, B2,2

214 rows, ouch!

38

We can determine where wumpus is!

• Method 2: Inference• Modus Ponens

• And-Elimination1,22,11,1

1,22,11,11,11 :

WWW

WWWSR

1,22,11,1 WWW

39

Inference continued...

• Modus Ponens and And-Elimination again:

• One more Modus Ponens:1,32,21,21,1

1,32,21,21,11,22 :

WWWW

WWWWSR

3,12,22,11,1

3,12,22,11,12,14 :

WWWW

WWWWSR

40

Inference continued...

• Unit Resolution:

3,1

2,1

3,12,1

2,2

3,12,22,1

1,1

3,12,22,11,1

W

W

WW

W

WWW

W

WWWW

Wumpus is in (1,3)!!!Shoot it. Shoot where?

41

Determining action based on knowledge

• Propositional logic cannot answer well the question “What action should I take?”

• It only answers “Should I take action X?”

ForwardForwardPA

ShootForwardWA

A

A

3,12,1

3,12,1

42

Propositional logic seems inefficient

• Rule: “Shoot if the wumpus is in front of you”• 16 x 4 = 64 rules for the 4x4 grid

• Ditto for pits

43

First-order logic to the rescue

• Uses variables to represent generalities• Can reduce rules significantly