2 - Knowledge Representation and Inference Paul Dunne GMITArtificial Intelligence 1 What is knowledge? Try to define it. –The study of knowledge is a called

Paul Dunne GMIT Artificial Intelligence 1

2 - Knowledge Representation and Inference

• What is knowledge? Try to define it.– The study of knowledge is a called epistemology.

• Knowledge can be further defined as – Procedural knowledge

• Knowing how to do something (eg knowing how to start a car.)– Declarative knowledge

• Knowing that something is true or false – Tacit knowledge

– eg I know how to put the key in the ignition but do I know how my hand/arm/muscles/tendons/nerves all corordinated?

Introduction Epistemology

Philosophicstudies

A prioriknowledge(universally

true andcan't bedenied)

A posterioriknowledge

(truth or falsityof the

knowledgeverifible by the

senses)

AristotlePlatoKantLocke



• AI suggests that intelligent behaviour can be achieved through the manipulation of symbol structures

• You could use this knowledge to infer new facts.– Galway has a new fire-engine.– It must be red!

• We represents facts (on the computer) using data structures and we write program code to reason with them.

Introduction

Red

Fire-EngineSymbols

Symbol Structure Red (Fire-Engine)



Knowledge Representation Languages

• High level knowledge representation languages have been developed to make knowledge representation easier

• We’ll look at a few of these – Semantic nets– Frames– Predicate logic– Rules



First though…Requirements for a knowledge representation language

• It must allow you represent adequately complex facts in a clear and precise yet natural way, and in a way that easily allows you to deduce new facts from your existing knowledge.– adequately complex facts

• Known as - Representational adequacy

– A level of detail that will produce the results we require and no more

» if a simple representation language will be adequate then use a simple language!

– dislikes (everybody, sprouts)



Requirements for Knowledge Representation Languages

– clear and precise• Known as - Well defined syntax and semantics

– no room for confusion and no ambiguities.– Syntax defines the allowable structures which describe how to

make sentences» “Dislikes – everybody – sprouts” is not allowed

– Semantics defines what it means» “dislikes (everybody, sprouts)” means everybody dislikes

sprouts not sprouts dislike everybody.

– Natural• Language must not be overly complex and difficult to

interpret.

– deduce new facts• Known as - Inferential adequacy

– The language must support inference.



The main contenders

• Broadly speaking there are three main approaches to knowledge representation in AI.– SEMANTIC NETS/FRAMES

• Easy to use and relatively natural.

– LOGIC• Arguably the most important. With a well defined syntax and

semantics. Allows inference but can be difficult to translate the real world into logic. Has difficulties with time, uncertainty and beliefs.

– RULES (If fire Then shout help)

• Condition-action rules or Production Rules(specifying what to do under certain conditions) within a rule-based system.

))()(( XfilesXbirdX



Semantic Nets/Frames



Semantic Networks

• Allows you to represent classes (or categories) of objects and relationship between objects and to draw simple inferences based on this knowledge.

• The net is made up of nodes and arcs/links connecting the nodes.

• The links express relationships. Without relationships knowledge is simply a collection of unrelated facts. – with them other knowledge can be inferred. (nellie has a head!)

• The nodes express physical objects, concepts or situations.

A simple class hierarchy

animal

reptile mammal

head

elephant

large grey

clyde nellie apples

subclass subclass

has-part

size colour

instance instance

likes

subclass

A concept

A relationbetween concepts

class

instance

Conclude: Clyde and Nellie both have heads



Semantic Networks

• Originally used to represent the meaning of English words • The links represent the relationships .

– The most important relations are;• known as a A-KIND-OF (AKO) relationship• known as a IS-A relationship

– Other relations also allowed• To represent properties of objects and categories of objects.

• Semantic networks normally allow efficient inheritance-based inferences using special purpose algorithms.

• Semantic nets in maths are labelled, directed graphs.• Sometimes known as associative nets (i.e. nodes are

associated or related to other nodes)



Semantic Networks

• Have a Go ! --- Class Problems– Represent each of the following useful pieces

of knowledge as a semantic net.• (a) “Floyd is a small hippo who lives in Dublin zoo.

Like all hippos he eats grass and likes swimming”

• (b) “The aorta is a particular kind of artery which has a diameter of 2.5cm. An artery is a kind of blood vessel. An artery always has a muscular wall, and generally has a diameter of 0.4cm. A vein is a kind of blood vessel, but has a fibrous wall. Blood vessels all have tubular form and contain blood.”



HIPPO

FLOYD

IS-A

grass

swimming

eats

likes

smallsize

Dublin zoolives

(a)

Blood Vessel

Artery

AKO

Fiborous Wall

Vein

AKO

Aorta

IS-A

2.5cm

diameter

Muscular Wall

Has-A

0.4cm

diameter

Has-A

Tubular FormBlood

Contain(b)



Semantic Networks

• To try and properly define the semantics of a semantic network (what it means) set theory is often employed.

• Semantic networks allows us to represent knowledge about objects and relationships between objects in an intuitive way. However the sort of inferences that can be supported is fairly restrictive

(just inheritance of properties). Also the lack of any standards for link names is problematic. A semantic net cannot define knowledge as well as logic can. There is no way to encode heuristic knowledge (rules of thumb) into

semantic nets.

• It remains a good choice as a knowledge representation language for some AI problems – particularly for showing binary relationships.



Frames

• Frames are a variant of semantic networks– popular way to represent facts in an expert system.

• The difference is basically in the level of detail of a node.– In semantic nets the node has a name.

• Properties of a node are shown using other nodes and some sort of relationship linking them.

– In a frame the node itself has a structure.• This means that the node can contain values or indeed other

frames.• Semantic nets (generally) represent knowledge about a broad area.• Frames represent (related) knowledge about a narrow subject • A frame would be a good choice for describing something such as a

car – a computer etc.



Frames• A frame is basically a group of slots (sometimes called properties) and

slot values or fillers) that define a stereotypical object.

Mammal:subclass: Animalhas_part: head

Elephant

subclass: Mammal

colour: grey

size: large

Nellie

instance: Elephant

likes: apples

3 Frames

Object

Slot

Slot value

Property

Infer Using InheritanceNellie is a large and grey, likes applesand has a head.

Property and Slot terminology is interchangeable

A slot value may also be a frame



Frames

• Some of the terminology from frames has been adopted by Oject Orientated technology.

• It is straight forward to translate between semantic networks and frame based representaion.– Class and Instance Nodes ---- Objects– Links ---- Slots– Node at end of Link --- Slot value



Semantic Net and Frame

animal

reptile mammal

head

elephant

large grey

clyde nellie apples

subclass subclass

has-part

size colour

instance instance

likes

subclass


Elephant

subclass: Mammal

colour: grey

size: large

Nellie

instance: Elephant

likes: apples



Defaults and Multiple Inheritance


Elephantsubclass: Mammal

colour: grey

size: large

Nellie

instance: Elephant

likes: apples

*furry: yes

*furry: no

Defaultvalue canbe over-ridden

•Objects inherit the default property value unless they have an individual property value that conflicts with the inherited one.

•Multiple inheritance is difficult and often results in conflicts.

•Nellie could be a circus-animal who has been specially “engineered” to be white. Nellie then is a subclass of Elephant and Circus-animal.

•Colour? The value for Elephant or for Circus-animal? •The system must provide for these conflicts – such that it will return the right value for colour (white) and the right value for size (large).



Practical Frames

• The slots and slot values can be frames.• The slot values could also be procedures, executed when

the value for the slot is required.– [The system is then described as having a procedural rather that

decalarative semantics]

• Implementation of a simple frame system could be carried out with the following algorithm [Note the recursion];– What is the slot value for object “O’s” slot P.

• value(O, P)– If slot name P exits for object O then

» Return slot value of P– Else if object O has slot called “subclass” or “instance”.

» Then return “Super”, the value of this slot – Find value(Super, P) and return this value.– Else Fail.



Frames and Semantic Nets Summary

• Frames and semantic networks provide a clear and simple way of representing properties of objects and categories of objects. A basic inference is available through inheritance.

• It does not cope will with– Negation ( not A)– Disjunction (A or B) – Quantification (for all A and some B)



Frames

• Go on try it.– Represent the following as frames;

• (a) “Hippos live in Africa. Hippos are generally quite large. Floyd is a small hippo who lives in Dublin zoo. Like all hippos he eats grass and likes swimming”

• (b) “The aorta is a particular kind of artery which has a diameter of 2.5cm. An artery is a kind of blood vessel. An artery always has a muscular wall, and generally has a diameter of 0.4cm. A vein is a kind of blood vessel, but has a fibrous wall. Blood vessels all have tubular form and contain blood.”



Frames

Hippo

likes swimming

eats grass

*lives Africa

*size large

Floyd

is-a Hippo

lives Dublin Zoo

size small

(a)

Blood-vessel

form tubular

contains blood

Artery

ako Blood-vessel

wall muscular

*Diameter 0.4cm

Vein

Ako Blood-vessel

Wall fiborous

Aorta

is-a Artery

Diameter 2.5cm

(b)



Logic



Logic

• Most important knowledge representation language is arguably (predicate) logic. – It allows us to represent fairly complex facts about the world, – To derive new facts in such a way that guarantees that if the initial

facts were true then so are the conclusions.

• The term “reasoning”, “inference” and “deduction” are generally used to cover any process by which conclusions are reached.

• Logic is a formal system which may be described in terms of its syntax, sematics and its proof theory.

• First we will look at the simpler propositional logic (sometimes called boolean logic) and then the more useful predicate logic



Propositional Logic

• Syntax– Symbols (P, Q, R, S, T ….) are used to represent facts

about the world.• “Paul is tall” represented by “P”• “Paul likes rugby” represented by “R”

– These simple facts are called atomic propositions.– You can build more complex sentences by combining

atomic propositions with logical connectives

• Paul is tall AND Paul likes rugby ( PR)• Paul is tall OR Paul likes rugby (P R)• Paul doesn’t like rugby (R)• If Paul is tall then Paul likes rugby ( P R)• If Paul is tall then Paul likes rugby and vice versa ( P R)

Note- The symbol TallPaul could also have been used

)(),(),(),(),( eequivalencnimplicatioNotOrAnd



Propositional Logic - Syntax

• Implications () are sometimes called conditionals or rules or if-then statements.

• Equivalence () is often called bi-conditional

• A sentence can be formed by combining simlper sentences with one of the five logical connectives.

• P Q• (P Q)

• The logical constants True and False are sentences by themselves

• A propositional symbol such as P or Q is also a sentence.

• Wrapping parentheses around a sentence yields a sentence eg (PQ).

RQP )(Premise or antecedant

Conclusion or consequence



Propositional Logic - Semantics

• The semantics of propositional logic allow us to state precisely what sentences like “P (PQ)” mean.

• It is defined in terms of what is true in the world. If we know P and Q are tue then semantic of the language will tell us if sentences like “P (PQ)” are true.

• We can determine the truth or falsity of sentences like these using truth tables.

X Y X V Y

True True True

True False True

False True True

False False False

If we have the assertion “raining V sunny” and the truth value of the assertion is true. Working backwards from the truth value of the sentence towards the constituent parts gives us the meaning of the sentence. Given the precise semantic of “V” we see that this means that it can be raining and it can be sunny when the sentence is true– without this precise semantics we may not have interpreted this correctly.



Propositional Logic - Semantics

P Q P PQ PQ PQ PQ

False False True False False True True

False True True False True True False

True False False False True False False

True True False True True True True

There does not have to be any relation or causation between P and Q. The following sentence is a true sentence of propositinal logic – althought its strange “English” sentence.

( 5 is an odd number) (Tokoyo is the capital of Japan)

Also an implication is true whenever its antecedant (P) is false!

(5 is an even number) (Spiddal is bigger then Rome)

Is true regardless of whether Spiddal is indeed bigger than Rome. Think of P Q as meaning “If P is true then I am claiming that Q is true. Otherwise I make no claims”.

The truth table for And and OR and Not are in close accord with our intutition of English words.

In some ways the the implication connective () is the most important and the most confusing. Confusing because it does not fit our intutive understanding of “P imples Q” ( or “If P Then Q”).



Propositional Logic – Validity and Inference

• Truth tables can not only be used to define the connectives but also to test for valid sentences.

• We make a row for each of the possibe combinations of truth values for the proposition symbols in the sentence. For each row we calculate the truth value of the entire sentence. If the sentence is true in every row then the sentence is valid. Consider ((PH)H) P

P H PH (PH)H ((PH)H) P

F F F F T

F T T F T

T F T T T

T T T F T



Propositional Logic – Proof Theory

• The process by which the soundness of an inference (such as ((PH)H) P ) is established through truth tables can be extended to entire classes of of inference. There are certain patterns of inference that occur over and over again – the soundness of this pattern can be shown for once and for all and captured in an inference rule which is universally valid.

• Once a rule is built then it can be used to make inferences without going throught the tedious process of building truth tables.

• There are many rules of inference here are two.

B

BAA ,

AVC

CBAVB ,

Modus Ponens

If AB is True and A is true then B is necessarily true.

If its raining then Paul puts on his coat. Its raining out then Paul has his coat on.

Resolution (somewhat like Prolog)

Since B cannot be both true and false, then A or C is true

Given “sunnyV raining, raining V carryumbrella” we can conclude “sunny V carrycumbrella”

Given this

Infer this



Predicate Logic

• Syntax– One problem with propositional logic is that it is not

possible to write general statements.• Paul likes everything

– Predicate calculus allows general statements– Sentences in predicate calculus are built up from

atomic sentences. This allows facts to expressed as a predicate name and some arguments.

• likes(paul, rugby)

– So rather than having a single proposition “P” to store the fact that “paul likes rugby” we have a predicate logic sentence “likes(paul, rugby)” where we can ‘get at’ the individual entities ‘paul’ and ‘rugby’



Predicate logic - Syntax

• The arguments in an atomic sentence may be any term, such as;• Constant symbols [lowercase such as “paul”]• Variable symbols [Uppercase such as “X”]• Function expressions [such as father(paul) which are composed of a functor

followed by arguments, which themselves can be any term]• Sentences can be constructed by combining atomic sentences with

logical connectives.• likes(paul, rugby) likes(paul, soccer)• likes(paul, movies) likes(paul, students)

• Sentences can also be formed using the quantifiers (existential quantifier - there exists) and (universal quantifier - for all). [Note: All variables should be quantified]

X(likes(paul,X) contact_sport(X)) ie There exists a contact sport paul likes X Y (person(X) likes(X,Y)) ie Everyone like something

Atomic sentences likes(paul, rugby) likes(paul, X) friends(father(paul), jim)



Predicate Logic - Semantics

• The semantics of predicate logic is defined in terms of the truth values of sentences (like propositional logic). Like propositional logic we can use the truth table to find the truth value of sentences involving logical connectives from the truth value of each part of the sentence.

• However we also need to deal with predicates, arguments and quantifiers. For simplicity assume that you can assign a truth value to a sentence like likes(paul, rugby)

• The meaning of can be defined in terms of whether some sentence is true for all objects in the domain of interest. X S means that for all X in a domain, S is true.

X likes(X, movies) could be verified if we could go to the domain under consideration (such as this class) and verify that likes(joe, movies), likes(jim, movies) etc.

• The meaning of could also be defined in terms of whether some sentences are true for at least one of the objects in the domain of interest.

• So if likes(jim, movies) was the only sentence we could show to be true then; X likes(X, movies) would be false X likes(X, movies) would be true.



Predicate Logic

• Inference rules in predicate logic are similar to those in propositional logic.

• Modus Ponens and Resolution still apply but in a slightly modified format to deal with variables and quantifiers.

• All this said the aveage AI programmer doesn’t have to know predicate logic semantics or proof procedures. – However they should know how to represent

things in predicate logic and what predicate logic expressions mean.



Predicate Logic

• Examples of English sentences converted to predicate logic– John loves Mary

• Use the verb as the prediate and the nouns as arguments– loves(john, mary)

– Mary is tall• Make a one argument predicate

– tall(mary)– If the car is moving then wear the seat belt

• Generally translate If X then Y into X Y– moving(car) wear(seat_belt)

– If Paul is hungry then he eats fruit– Hungry(paul) eats(paul, fruit)

– All Students study X student(X) study(X)

– These is something small and slimey on the floor X ((small(X) slimey(X) onfloor(X))



Logic and Prolog

• The most widely used logic programming language is Prolog. It is based on predicate logic.

• Each statement in a Prolog program corresponds to a sentence in predicate logic.

• The notations are different however and Prolog will only allow a horn clause [only one fact allowed on the right hand side of an implication sign]. This allows a simpler and more efficient goal directed proof procedure to be executed by Prolog.

• The Prolog system views your (Prolog) computer program as a set of statements in logic. You then ask the system to prove a statement given the statements in your program.

father(jim, fred)

father(joe, jim)

XYZ((father (X,Z) father(Z,Y))

grandfather(X,Y)

father(jim, fred).

father(joe, jim).

grandfather(X,Y) :-

father (X,Z), father(Z,Y).

Predicate Logic Prolog program

If Prolog was asked “grandfather(joe, fred)” it would repsond “true”.



Logic

• Logic is not only used as a knowledge representation language but also;– To communicate AI theories within the AI

community– As a basic of AI programming languages– To give the meaning of natural language

sentences in a natural language understanding system.

– To define the semantics of other simpler representation languages (such as frames).



Logic Summary

• Predicate logic is a powerful way to represent and reason with knowledge.

• Negation, disjunction and quantification are easily represented using logic (which is not true for frames)

• Available proof procedures and inference rules means that a very wide range of inferences are possible (contrast this with frames where only simple inheritance based inference is possible)

• Logic has a problem in dealing with uncertainty, defaults and beliefs. Where new logic has been developed to deal with these issues the logic can become overly complex.



Logic - Questions

• Give it a go.– Convert the following to the language of

predicate logic.• Every apply is either green or yellow

• No apple is blue

• If an apple is green then its tasty

• Every man likes a tasty apple

• Some people like garlic

• Fido is a doberman and a good dog.

• All basketball players are tall



Logic - Questions

Convert the following to the language of predicate logic.• Every apply is either green or yellow

• No apple is blue

• If an apple is green then its tasty

• Every man likes a tasty apple

• Some people like garlic

• Fido is a doberman and a good dog.

• All basketball players are tall

))()()(( XredXgreenXappleX

))()(( XbluexappleX

))()(( XtastyXappleX

)),()()(( YXlikesYtastyAppleXmanYX

)),()(( garlicXlikesXpersonX

)()( fidogooddogfidodog

))()(( XtallXPlayerbasketballX



Rule Based Systems



Rule-Based Systems

• Instead of representing knowledge in a relatively declaratively, static way (as a set of things that are true) rule based systems represent knowledge as a set of rules for different situations that

– tell you what to do

– or what you can conclude

Control Scheme (Intepreter – controls application of rules)

Condition action rules

IF alarm_beeps THEN

ADD smoky

IF hot AND smoky THEN

ADD fire

Database of facts

(normally representing things that are true)

alarm-beeps

hot

Note: IF-THEN rule based systems are independent chunks of knowledge, to be invoked, as required, by the interpreter. In C or Java they are treated as a sequence of instructions. They are like implications in logic, alarm_beeps smoky .



Rule-Based Systems

• The interpreter can use one of the following methodologies (reasoning mechanims) to connect a problem with a solution. This is called inference.

• Forward chaining (CLIPS and Jess)• Start with some initial facts and the interpreter keeps using rules to

draw new conclusions (or take certain actions) given those facts.• Useful when you know facts but don’t know what conclusions can be

drawn (or what likely conclusions can be drawn) – “The ground is wet. What might be happening”?…

– Backward chaining (PROLOG)• You start with some hypothesis (or goal) you are trying to prove and

keep looking for rules that allow you to conclude that hypothesis – possibly setting new subgoals to prove as youi go along.

• Focus on a hypothesis.– “Should I wear a raincoat”

• Chaining gets it name from chaining inferences (modus ponens) together to form a chain of inference.

– elephant(X) mammal(X)– mammal(X) animal(X)



Forward and Backward chaining

R2 R3 R4R1

R5 R6 R7

R8 R9

A B C D E F G

HH

I

H

J JK

Initial Facts - Given

Intermediate fact

CONCLUSIONS(Could be new facts , output etc)

BO

TT

OM

-UP

H

H1 H2 H3

H4 H6H5

A B C D E

InitialHypothesis

IntermediateHypothesis(sub goals)

Evidence

The original hypothesis may beproved by the evidence

AND

AND

AND

Top

Dow

n



Forward Chaining and Backward Chaining comparison

Forward Chaining Backward Chaining

Planning monitoring and control Diagnosis

Present to future Present to past

Antecedent to consequence Consequenc to antecedent

Data driven, bottom up reasoing Goal –driven , top down reasoning

Work forward to find what solutions follow from the facts

Work backwards to find facts that support the hypothesis

Good for breadth first search Good for depth first search

Antecedents determine where the search goes

Consequences determine search

Exaplanations are not easily facilitated Explanation facilitated



Forward chaining rule-based systems

• Facts are held in working memory which is being continually updated as rules are invoked.• Rules represent possible actions to take when specified facts occur in the working memory.• The interpreter controls the application of the rules.

Working Memory Stores facts (positive literals no variables)

InterpreterControls Application of Rules

Condition-Action Rules

IF ... THEN ADD ...IF ....THEN DELETE...IF....THEN PRINT....

Current Facts

Add New Facts

Delete FactsPrint

Message



Forward chaining rule-based systems

• The interpreters cycle of activity is sometimes known as the recognize-act cycle.– Fire a rule

• Which rules conditions (IF parts) hold given the current state of working memory. (Match phase)

• Select a rule (Conflict resolution phase)• Perform action in conclusion of rule (THEN part)

which may modify working memory (Act phase)

– New working memory results– Repeat (until no rule fires or Halt encountered)



Forwad chaining rule-based systemsExample

Working Memory F1: alarm_beeps F2: hot

InterpreterControls

Application ofRules


R1: IF hot AND smoky THEN ADD fireR2: IF alarm_beeps THEN ADD smokyR3: IFfire THEN ADD switch_on_spinklers

Current Facts

Add New Facts

Delete FactsPrint

Message

Working Memory F1: alarm_beeps F2: hot F3:smoky

InterpreterControls

Application ofRules



Current Facts

Add New Facts

Delete FactsPrint

Message




Working Memory F1: alarm_beeps F2: hot F3:smoky

InterpreterControls

Application ofRules



Current Facts

Add New Facts

Delete FactsPrint

Message

Working Memory F1: alarm_beeps F2: hot F3:smoky F4:fire

InterpreterControls

Application ofRules



Current Facts

Add New Facts

Delete FactsPrint

Message




Working Memory F1: alarm_beeps F2: hot F3:smoky F4:fire

InterpreterControls

Application ofRules



Current Facts

Add New Facts

Delete Facts

Sprinklers

The example illustrates that the order in which rules fire depends on what is in working memory, and not on the sequence of the rules.

A problem arises when more that one rule can fire based on what is in working memory.

F1: alarm R1: If alarm THEN fight_fire

F2: evacuate R2: If alarm THEN evacuate

It is very important which rule is chosen to fire when there is a choice!



Forward chaining

• Conflict resolution strategy – A forward chaining system will have some conflict resolution strategy to decide which rule to

fire. Common strategies are;

• Prefer to fire rules that involve facts that have been recently added to working memory

• Prefer to fire rules that have more specific conditions. (eg IF a AND b AND c THEN d instead of IF a THEN z).

• Allow the user to prioritize rules.

• Fire all applicable rules at once.

• Reason maintenance

– Some sophisticated techniques have been developed to to update working memory to remove facts whose justification for being there has become invalidated. (The facts that caused the rule to fire to add this fact no longer hold => no justification for this fact to be in the working memory).

• Pattern matching– If we have more complex fact, temperature(kitchen, hot) and we want to match it

aginst a general rule, IF temperature(R, hot) THEN alarm, then we will employ pattern matching (matching the pattern temperature(kitchen, hot) against IF temperature(R, hot) THEN alarm) which will greatly increase the flexability of our rules.

Depth First

(CLIPS default)

Breadth First



Forward chaining – Expert systems

• CLIPS– One expert system tool based on forward chaining is

CLIPS (C language Integrated Production System)

– Allows a wide variety (7) of conflict resolution strategies to be selected and limited facilities for reason maintenance.

• Jess– An expert system shell (essentially implements CLIPS

in Java). Jess Supports the development of rules based expert systems. Jess v6.0 is compatible with Java 1.2 and in particular the JDK 1.3.



Backwards chaining

• Suppose you have a hypothesis to test, then forward chaining systems may not be most efficient way of determinig the truth of your hypothesis.

• The forward chaining system would keep on chaining until no more rules applied or until your hypothesis was added to the working memory.

• Ultimately a lot of of unnecesary conclusions would be added to the working memory.



Backwards chaining

– R1: IF smoky AND hot THEN ADD fire– R2: IF alarm_beeps THEN ADD smoky– R3: IF alarm_beeps THEN ADD ear_plugs– R4: IF fire THEN ADD switch_on_sprinklers– R5: If smoky THEN ADD poor_visibility– F1: alarm_beeps– F2: hot

• In a forward chaining system the following facts would be added• Smoky, fire, ear_plugs, switch_on_spinklers, poor_visibility

– This would be overkill if were simply interested in knowing whether we should switch on the spinklers.

• Backward chaining focuses on the hypothesis in question.– You start with a goal we want to prove

• switch_on_spinklers

– System checks if the goal matches any of the given facts – if then does then the goal succeeds. If not then the system will look at the rules actions (conclusions) and see if any of those match the goal.

– If the conclusion matches the goal the system will then try to pove the preconditions of the rule (in effect a new sub-goal has been defined).

– Backward chaining systems keep track of goals that they are trying to prove (they do not need to update a working memory)



Backward chaining - Example

• The initial goal is;– G1: switch_on_spinklers

• Not in initial facts• Matches conclusion R4 > G2

– G2: fire• Not in facts• Matches conclusion R1 > G3, G4

– G3: smoky G4: hot• G3 Matches conclusion of R2 > G5

– G4: hot G5: alarm beeps• G5: Matches facts • G4 : Matches Facts• > G3 satisfied• > G2 satisfied• > G1 satisfied !!!

R1: IF smoky AND hot THEN ADD fireR2: IF alarm_beeps THEN ADD smokyR3: IF alarm_beeps THEN ADD ear_plugsR4: IF fire THEN ADD switch_on_sprinklersR5: If smoky THEN ADD poor_visibilityF1: alarm_beepsF2: hot

switch_on_spinklersR4

fireR1

smokyR3

hotF2

alarm_beepsF1

G1

G2

G3 G4

G5



Backward chaining - Implementation

• A backward chaining system may be implemented using a stack to record the goals that are still to be satisfied. You repeatedly try to pop a goal ff a stack to try and prove it. If its in the initial set of facts – its proved. If its matches a rules conclusions then the preconditions are pushed onto the stack as new goals.

• The overall goal succeeds if all the sub goals are removed off the stack.

• If more than one rules conclusions could be matched against the goal then search techniques must be employed.

G5

G4

G3

G2

G1???

Note:

Prolog uses backward chaining (with depth first search) to try and prove things. This makes it a good choice for prototyping simple expert systems.



Summary

• Knowledge representation languages provide high level representation formalisms to represent the knowledge required for AI problem solving.

• A good language should be natural, clear and precise, allow you to represent what is required, and support the sound inference of new facts.

• Frames and semantic nets represent knowledge as an organised collection of objects with attributes, arranged in a hierarchy. If an object is a sub class of another it may inherit its attributes. They are limited in what can be represented and inferred, but provide a natural and efficient representation scheme.

• A logic, and particular predicate logic, may be used as a precise and formal language able to represent a fairly wide range of things. A Logic may also be used to describe the semantics of other formalisms.

• Rule based systems allow knowledge to be represented as a set of more or less independent IF-THEN or condition action rules, statting what action to take given different conditions. Reasoning can be controlled using a forward or backward chaining interpreter.

Documents

2 - Knowledge Representation and Inference Paul Dunne GMITArtificial Intelligence 1 What is knowledge? Try to define it. –The study of knowledge is a called