Chapter 7

Instructor : Miss Mahreen Nasir

Outline

Knowledge-based agents

Logic in general

Propositional (Boolean) logic

Equivalence, validity, satisfiability

Predicate Logic

Sememtic Networks

Frames

Logical Agents

Knowledge-based agents – agents that have

an explicit representation of knowledge that

can be reasoned with.

These agents can manipulate this

knowledge to infer new things at the

“knowledge level”

Knowledge Based AgentThe central component a knowledge-based agent is

its Knowledge base (KB) : set of sentences in a

formal language (i.e. a list of facts that are known to

the agent).

Each sentence is expressed in a language called a

knowledge representation language, and represent

some assertion about the world

Knowledge Bases

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 :

Knowledge level - i.e., what they know, what its goals are, in order to fix its behavior, regardless of how implemented

Implementation level i.e., data structures in KB and algorithms that manipulate

them

Each time the agent program is called:

1.It TELLs the KB what it perceive.

2.It ASKs the KB what action it should perform (query).

3.The agent program TELLs the knowledge base which action

was chosen and the agent executes the action.

A Simple knowledge based Agent

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

What is a Logic?Logics are formal languages for representing information

such that conclusions can be drawn.

Have a syntax and semantics

Syntax

How to make sentences, valid strings of sentences

Rules for constructing legal sentences in the logic

Semantics

Define the meaning of the sentences

How we interpret sentences in the logic

Logic-Syntax & SemanticsExample: Arithmatic language

Syntax: x+y=4 a well formed sentence

X2y+= not a well formed sentence

x + 2 >= y is true if and only if the number of x + 2 is no less than

the number y

x +2 >= y is true in a world (or model) where x = 7, y = 1

x +2 >= y is false in a world (or model) where x = 0, y = 6

Propositional Logic

Propositions: assertions about an aspect of a world

that can be assigned either a true or false value.

e.g. Sky is cloudy, Sarah is happy, Is morning, P1, ..

True, False are propositions meaning true and false

Atoms/atomic sentences:

composed of a single propositional symbol

e.g. Sky is cloudy

Propositional LogicComplex Sentences:

constructed of simpler sentences using logical

connectives (disjunction, implication, equivalence,

negation),

e.g. Sky is cloudy ∧ Sarah is happy.

Sentences Literals:

Either an atomic sentence (P1, positive literal) or a

negated atomic sentence (¬P1, negative literal)

Propositional Logic -SyntaxThe proposition symbols P1, P2 etc are (atomic)

sentences

If S is a sentence, (S) is a sentence (negation)

If S1 and S2 are sentences, (S1 S2) is a sentence

(conjunction)

If S1 and S2 are sentences, (S1 S2) is a sentence

(disjunction)

If S1 and S2 are sentences, (S1 S2) is a sentence

(implication)

If S1 and S2 are sentences, (S1 S2) is a sentence

(biconditional)

Propositional Logic -SementicsEach model specifies true/false for each proposition symbol

false true falseWith these symbols, 8 possible models, can be enumerated automatically.

Rules for evaluating truth with respect to a model m:S1 S2 is true iff S1 is true and S2 is true

S1 S2 is true iff S1is true or S2 is true

S1 S2 is true iff S1 is false or S2 is true

i.e., is false iff S1 is true and S2 is false

S1 S2 is true iff S1S2 is true and S2S1 is true

Simple recursive process evaluates an arbitrary sentence, e.g.,

P1,2 (P2,2 P3,1) = true (true false) = true true = true

S is true iff S is false

E.g. P1,2 P2,2 P3,1

Truth Table for Connectives

English to Propositional Formulae

Example 1 :

“It is not the case that the Sky is Blue ” :¬ B

( alternatively teh sky is not blue )

“The Sky is Blue and the Grass is Green ” :B ∧ G

“ Either teh sky is Blue or the Grass is Green ” :B ∨ G

“ If the Sky is Blue, then the Grass is not Green” :B→ ¬ G

“ The Sky is Blue if anf only if the Grass is Green ” :B↔ G

“ If the sky is blue,then if the Grass is not Green,the Plants

will not Grow ” :B→ ( ¬ G→ ¬ P )

English to Propositional Formulae

p = “It is below freezing”

q = “It is snowing”

It is below freezing and it is snowing

It is below freezing but not snowing

It is not below freezing and it is not snowing

It is either snowing or below freezing (or both)

If it is below freezing, it is also snowing

It is either below freezing or it is snowing,

but it is not snowing if it is below freezing

That it is below freezing is necessary and

sufficient for it to be snowing

pqp¬q¬p¬qpqp→q

((pq)¬(pq))

p↔q

Truth Table

•Truth tables can be used to test sentences for validity

• One row for each possible combination of truth values for the

symbols in the sentence

•Given n symbols,2^n possible

combinations of truth value assignments.

•Here each row is an interpretation

Truth Tables-Implications

•Does A⇒B is equivalent to ¬A ∨ B?•A⇒B is true iff A is false or B is true•is false iff A is true and B is false

•Implication is used in propositional logic and predicate logic to describe a relationship between two propositions or sentences.

Truth Tables-Validity

Truth Tables -Satisfiability

Truth Tables-Unsatisfiability

Predicate LogicPropositional logic combines atoms

An atom contains no propositional connectives

Have no structure (today_is_wet, john_likes_apples)

Predicates allow us to talk about objects

Properties: is_wet(today),is _a_bird(x)

Relations: likes(john, apples)

True or false

In predicate logic each atom is a predicate

e.g. first order logic, higher-order logic

First Order Logic

More expressive logic than propositional

Constants are objects: john, apples

Predicates are properties and relations:

likes(john, apples)

Functions transform objects:

likes(john,

Variables represenfruit_of(apple_tree))t any object: likes(X,

apples)

Quantifiers qualify values of variables

True for all objects (Universal): X. likes(X, apples)

Exists at least one object (Existential): X. likes(X, apples)

Example: FOL Sentence“Every rose has a thorn”

For all X

if (X is a rose)

then there exists Y

(X has Y) and (Y is a thorn)

Example: FOL Sentence“On Mondays and Wednesdays I go to John’s

house for dinner”

Note the change from “and” to “or”– Translating is problematic

Non-Logical Representations

Production rules

Semantic networks

Conceptual graphs

Frames

Logic representations have restricitions

and can be hard to work with

Production Rules Rule set of <condition,action> pairs

“if condition then action”

Match-resolve-act cycle

Match: Agent checks if each rule’s condition holds

Resolve:

Multiple production rules may fire at once (conflict set)

Agent must choose rule from set (conflict resolution)

Act: If so, rule “fires” and the action is carried out

Working memory:

rule can write knowledge to working memory

knowledge may match and fire other rules

<condition،action> قاعدة تعيين من أزواج

اذا كان الشرط ثم العمل""

دورة ACT-مباريات لحل

المباراة: وكيل الشيكات اذا كان الشرط يحمل كل قاعدة في

حل:

قد قواعد إنتاج متعددة اطالق النار في وقت واحد )مجموعة النزاع(

يجب اختيار وكيل حكم من مجموعة )حل النزاعات(

القانون: إذا كان األمر كذلك، حكم "حرائق" ويتم تنفيذ اإلجراء من

الذاكرة العاملة:

يمكن كتابة قاعدة المعرفة اللذاكرة العاملة

قد تطابق المعرفة وإطالق قواعد أخرى

Production Rules Example

IF (at bus stop AND bus arrives) THEN action(get on

the bus)

IF (on bus AND not paid AND have oyster card)

THEN action(pay with oyster) AND add(paid)

IF (on bus AND paid AND empty seat) THEN sit

down

conditions and actions must be clearly definedcan easily be expressed in first order logic!

Graphical Representation

Graphs easy to store in a computer

To be of any use must impose a formalism

Jason is 15, Bryan is 40, Arthur is 70, Jim is 74

How old is Julia?

Semantic Networks

Because the syntax is the same

We can guess that Julia’s age is similar to

Bryan’s

Semantic Networks

Used as an alternative to predicate logic for

knowledge representation

Knowledge is stored in the form of Graph

Nodes represent objects in the world

Arcs represent relationships between the objects

Semantic Networks

Conceptual Graphs

Semantic network where each graph represents a single proposition

Concept nodes can be

Concrete (visualisable) such as restaurant, my dog Spot

Abstract (not easily visualisable) such as anger

Edges do not have labels

Instead, conceptual relation nodes

Easy to represent relations between multiple objects

Frame Representations

Semantic networks where nodes have structure

Frame with a number of slots (age, height, ...)

Each slot stores specific item of information

When agent faces a new situation

Slots can be filled in (value may be another frame)

Filling in may trigger actions

May trigger retrieval of other frames

Inheritance of properties between frames

Very similar to objects in OOP

Example: Frame Representation