lecture 6 knowledge representation (1)

8/13/2019 Lecture 6 Knowledge Representation (1)

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Foundations ofKnowledge-based Systems

Lecture 2


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Outline

Recap Knowledge Representation

Propositional Logic

Predicate Logic

Validity and Soundness


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Recap Definition of KBS A knowledge based system (KBS) is a software system

capable of supporting the explicit representation ofknowledge in some specific competence domain and ofexploiting it through appropriate reasoning mechanismsin order to provide high-level problem-solvingperformance.

KBS is a specific, dedicated, computer-based problem-solver, able to face complex problems, which, if solved byman, would require advanced reasoning capabilities, suchas deduction, abduction, hypothetical reasoning, model-

based reasoning, analogical reasoning, learning, etc.

Typical problems Diagnosis Scheduling Planning


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Recap Components of a KBS

Knowledge Base

Problem

Domain Knowledge

Reasoning Mechanism

Working Memory

Solution Knowledge-Based

System


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Knowledge Classification Knowledge can be classified into

Priori knowledge: Universally true and cannot bedenied without contradiction. Examples are mathematical laws, logical statements.

Posteriori knowledge: Represents information that is

verified using sensory experiences. This Knowledge can be denied based on new knowledge

without the need for contradictions.

Further classification includes Procedural knowledge: Knowing how to do something.

Declarative knowledge: Knowing that something istrue or false.

Tacit knowledge: Unconsciously knowing how to dosomething.

Explicit knowledge:


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Knowledge Representation

This is the way that knowledge is stored in aprogram. This implies that

There is a systematic way to store the information.

The knowledge is coded into the program.

Knowledge representation and reasoning - thestudy of formal ways of extracting informationfrom symbolically represented knowledge

Existing computer languages can be used and the

knowledge is stored in memory.

The stored knowledge and facts can be used inreasoning.


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Knowledge Representation

Knowledge can be represented in a varietyof ways.

The predominant knowledge

representation schemes are Frames and production rules.

Connections and weights.


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Knowledge Representation Some desirable features of any knowledge

representation scheme include: Completeness:Should support the acquisition of all

aspects of the knowledge.

Conciseness: Allow efficient acquisition so that

knowledge is stored compactly and is easily retrieved. Computational efficiency:It should be possible to

use the knowledge rapidly and without the need forexcessive computation.

Transparency:Should be such that it is possible to

understand its behaviour and how it arrives atconclusions.

Explicity:The important things should be explicit butthe details suppressed but available in case it is

required in future.


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Why use special tools

Traditional languages emphasize Efficiency

Maintainability

Portability

Not representational power

Traditional language control is

Primitive

Implicit in statement ordering

Pretty much fixed at compile time Good for algorithmic work, but knowledge is

implicit not explicit.


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Why use special tools

There is no single representation scheme that embodiesall the above characteristics.

Each of the representation schemes is suitable for certaintypes of application domain.


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Types of representation schemes

Some popular representation schemes include

Rule-based schemes:Information is stored asabstract rules that have general applicability.

Learning is explicit.

Instance based models:Do not operate on explicitrules. Exhibit rule-like behavior by being exposed to aseries of examples.

Learning is implicit.


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Logic and other schemes

Logic:Extensively used in Al programs.

Main purpose of logic: The soundness or unsoundness ofarguments.

Typically, an argument consists of statements calledpropositions, from which other statement(s) calledconclusion(s) are claimed to follow.

This is the basis of propositional logic.


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Propositional Logic

Proposition:A sentence that is either true orfalse.

Example: The following are propositions:

Sam is a happy man" (1)

"All cats are good pets" (2)

Propositions, because each is either true or false.

The following phrases are not propositions:

"Amy's pet" (3)

"Oh dear me!" (4)

Statements in propositional logic are usuallyexpressed symbolically.


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Propositional Logic

Example:

The following inference:

"If Sam is a happy man then Sam is a teacher"

Could be symbolically expressed as:

A: Sam is a happy man B: Sam is a teacher

This could be expressed in propositional logic as:

if A then B

Logic notation: A B (meaning proposition Aimplies proposition B).


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Propositional Logic

This is an example of a rule of inference called modus

ponens.

This says that if propositionAis true, and the rule ofinferenceA Bis true, then Bwill also be true.

Propositions can be combined using logical connectivese.g. "If I listen to music and the room is warm then I fall asleep

Rewriting this symbolically: PropositionA: I listen to music

Proposition B: The room is warm

Proposition C: I fall asleep


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Propositional Logic

Then this can be written in logic notation as:

A B C

Connective symbols

The symbols shown in the table are used to denote someof the most common connectives used in propositionallogic.


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Propositional Logic

Symbol Meaning Interpretation-A

A B

A B

A B

Not A

A and B

A or B

A implies B

Negation. Negation of propositionAis true ifAis false and vice versaConjunction. Aand Bonly true ifA

and Bare both true, otherwise falseDisjunction. Aor Bis true ifAistrue or Bis true.Implication. IfAis true andAimplies Bis true, then Bis true. IfA

is false andAimplies Bis true thenanything goes. That is, Bcould betrue or false, since implication saysnothing about case whenAis false


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Propositional Logic

Truth table

The meanings of the connectives and their results aresummarized in the table

A B A A B A B A B1100

1010

0011

1000

1110

1011


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Predicate Logic

Propositional logic is inadequate for solving some

problems because a proposition has to be treated as asingle entity that is either true or false.

Predicate logic overcomes this by allowing a proposition

to be broken down into two components. Arguments

Predicates.

It allows the use of variables, in addition to supporting

the rules of inference derived from propositional logic(i.e. modus ponens etc.).


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Predicate Logic

Example

Consider the proposition:

Kamau has brown hair.

This could be written in predicate logic notation

as: HAS (Kamau, short hair)

In the example,

Predicate: HAS Arguments: Kamau and brown hair.


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Predicate Logic

Quantifiers in predicate logic

Predicate logic also allows for the use ofquantifiers.

This means that the language can be extended to

propositions that refer to a range of a variable. For example, consider the proposition:

Every man loves a woman.

This can be expressed in predicate logic using

quantifiers as:


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Predicate Logic

x, Man(x) y, s.t. Woman(y) Loves(x, y)

Which reads: For any object xin the world if xis a Man, then there exists an

object y, such that yis a woman and xLoves y.

Quantifiers

: The universal quantifier since it refers to all objects inthe (male) population.

: The existential quantifier since it refers to at least oneobject in the (female) population.


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Predicate Logic

Now consider the proposition: every Welshman is a Man.

This would be expressed in formal logic as:

x, Welshman(x) Man(x)

Which reads: for any object x, if xis a Welshman, then xis a man.


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Predicate Logic

Then from the two facts it can be concluded, using the

rules of inference, that the following fact must be true:

x, Welshman(x) y, s.t. Woman(y) Loves(x, y)

That is, every Welshman loves a woman.

The example seems to lead to an obvious conclusion.However, for other examples such intuitive conclusions

would be less obvious.


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Logic: Validity and Soundness

Consider the following deductive argument:

If you are in Chiromo, then you are in Nairobi

If you are in Nairobi, then you are in Kenya

Therefore if you are in Chiromo you are in Kenya

Both premises and conclusion happen to be true

statements, But if you substitute Kampalafor Nairobi theargument will have false premises.

Therefore, there are arguments that intuitively seem tobe valid in the sense that the conclusions somehow

follow from the premises, but which still have somethingmissing.


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Logic: Validity and Soundness

Validity:

A deductive argument (or argument form) is valid ifand only if it is impossible for its conclusion to be falsewhen its premises are true.

Soundness:

A deductive argument is sound if it is valid and hastrue premises.


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Advantages of formal logic

There is a set of rules called rules of inferenceby which

facts that are known to be true can be used to deriveother facts, which must also be true.

The truth of any new proposition can be checked, in a

well-specified manner, against the facts that are alreadyknown to be true. Logical inferences will only guarantee the truth of a conclusion if

the premises leading to the conclusion are also true.


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Summary

Knowledge Base Systems

Components

Types

Knowledge Classification

Knowledge Representation Propositional Logic

Predicate Logic

lecture 6 knowledge representation (1)

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