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241-320 Design Architecture and Engineeringfor Intelligent System

Suntorn Witosurapot

Contact Address:Phone: 074 287369 or

Email: [email protected]

November 2010

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Lecture 10:

Knowledge Representationand Reasoning Part 1

( )

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241-320 Design Architecture &Engineering for Intelligent System

Knowledge Representation andReasoning - part 1

3

Preview

Our last lectures were all focused on algorithms thatallow you to develop smart software

Smart = intelligence, e.g.

Find optimal solutions according to given scenario

Find the shortest path

Suggest on step to proceed in adversrial game thathas more chance to win

etc.

In this lecture, we move our focus from problem-specific agents to knowledge-based agents

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Knowledge Representation andReasoning - part 1 4

Preview (cont.)

Knowledge-based Agents

Can representknowledge

And reasonwith this knowledge,

Can combine general knowledge with currentpercepts to infer hidden aspects of the current state

Q: How is this different from the knowledge used by

problem-specific agents?

more general

more flexible

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Preview: Knowledge bases

Knowledge base = set of sentences in a formal language

Allows an agent to reason about the world, deduce hiddenproperties and determine appropriate actions.

Example:KB = {Somchai comes to the party;

If Somsri comes to the party then Somying comes;

If Somsri doesn't come then Somchai won't come to the party }

Agent should be able to deduce that .... Somying comes to the party.

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Preview: Knowledge representation(KR)

Any agent can be described on different levels:

Knowledge level (knowledge possessed by agent)

Logical level (algorithms for manipulating knowledge)

Implementation level (how algorithms are implemented) Knowledge Representation is concerned with

expressing knowledge explicitly in a computer-tractable way (for use by the agent in reasoning)

Reasoning attempts to take this knowledge and drawinferences (e.g. answer queries, determine facts that followfrom the knowledge base, decide what to do, etc.)

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Outline

Knowledge vs Data

Knowledge RepresentationSchemes

Logic-based Knowledge Representation Propositions

Propositional Logic

Syntax

Semantics First-order Logic

Conclusion

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Information Hierarchy

Data

The raw material of information

Information

Data organized and presented in a

particular manner

Knowledge

Justified true belief

Information that can be acted upon

Wisdom Distilled and integrated knowledge

Demonstrative of high-levelunderstanding

Data

Information

Knowledge

Wisdom

More refined and abstract

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An Example

Data

98.6 F, 99.5 F, 100.3 F, 101 F,

Information

Hourly body temperature: 98.6 F, 99.5 F, 100.3 F,101 F,

Knowledge

If you have a temperature above 100 F, you most

likely have a fever

Wisdom

If you dont feel well, go see a doctor

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Why do we need formal languages for KR?

RECALL: Knowledge base = set of sentences in a formal language

Consider an English sentence like:

The boy saw a girl with a telescope

- 2 possible meanings:

- . . - . .

Also:

I heard about him at school (structural ambiguity)

- What are 2 possible meanings??

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Why do we need formal languages for KR?(cont.)

Natural languages exhibit ambiguity

Ambiguity makes it difficult for us to

to understand what is the intended meaning of

certain phrases and sentences, and also

to make inferences

This is why it does have Symbolic logic()

to support the ambiguity of the natural language a syntactically unambigious knowledge representation

language through the means of Symbol ( )

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Syntax vs. Semantics

Syntax () Describes the legal sentences ina knowledge representation language (e.g. in thelanguage of arithmetic expressions x

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Outline

Knowledge vs Data

Knowledge Representation Schemes


Propositional Logic

Syntax


Conclusion

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Knowledges Representation Techniques

There are three basic techniques for representing theacquired knowledge in a knowledge base

1. Logic-based representation ()

(Propositional) Logic

2. Object-based representation ()

Semantic Networks, Frames

3. Rule-based representation () Production Rules

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Outline

Knowledge vs Data



Propositional Logic

Syntax


Conclusion

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Logic-based Knowledge Representation

Logic (): (T) (F) Can be used as a formal language for representing

information such that conclusions can be drawn

This logical-based approach represents knowledge ina declarative, static way (i.e. as the form of sentence)so that they can be used and determined later

This is the basis of the programming languagePROLOG (Programming in Logic)

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What is a Logic?

A logic consists of

1. A formal system for expressing knowledge about adomain consisting of

SyntaxSet of legal sentences (also known asPropositions or)

SemanticsInterpretation of legal sentences

2. A proof system for specifying how we can derivederive new sentences from our existing sentencesIn a knowledge base

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241-320 Design Architecture &Engineering for Intelligent System Knowledge Representation andReasoning - part 1 18

Propositions ()

Propositions are entities (facts or non-facts) that canbe true or false ()

Propositions are expressed using ordinary declarative

sentences e.g. the sentence

expresses the proposition () that . Is this proposition true?

()

4 ()

These are called Single Proposition (),whereonly one subject and verb are in the sentence.

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Propositions () (cont.)

Other propositions (Complex propositionor),where prepsotions are involved to join sentences:

()

()1

4 ()

()

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Outline

Knowledge vs Data



Propositional Logic

Syntax


Conclusion

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Propositional Logic ()

(T) (F)

Logical Process

()

OutputInput

Facts(

)

Inferences

()

orConclusions

()

Example of the propositions using a simple deductive process

Statement A = The mail carrier comes on Monday through Friday.

Statement B = Today is Sunday.

Conclusion C = The mail carrier will not come today.

Premises()

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Propositional Logic ()(cont.)

All humans have 2 eyesJane is a humanTherefore Jane has 2 eyes

All humans have 4 eyesJane is a humanTherefore Jane has 4 eyes

All humans have 2 eyesJane has 2 eyesTherefore Jane is human

No human has 4 eyesJane has 2 eyesTherefore Jane is not human

Both are (logically) correctsentences Both are (logically) incorrectsentences

Which statements are true/false? Which statements are true/false?

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Propositional Logic

Often use single letters or symbols to representbasic propositions in reasoning

combine them into more complex sentences using

operators for not, and, or, implies, iff

Propositional connectives():

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From English to Propositional Formulae

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Improving Readability

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Semantics

The semantics of the connectives can be given bytruth tables

One row for each possible assignment of True/Falseto propositional variables

Note:Above Pand Qcan be anysentence,including complex sentences

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Limitations of Propositional Logic

Propositional logic is extremely simple, hence it haslimited expressive power and dificult to representstatements concerning objects and relations.

Example: How do we use propositional logic to

represent a general statement {} To do so we would need to have a separate proposition for

each person living on Earth claiming that she or he is moral.

{_, _, _, and so on}

This results in a huge number of separate propositions andthus causes problems of complexity with inference.

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Limitations of Propositional Logic (cont.)

Moreover, This kind of logic can only expresses truthor falsehood of a sentence.

So, it can not help us to express relationships between

objects, e.g. Father(Bob,BobJr)

So, we need a more expressive logic (like First-orderlogic) that allows us to reason about objects, theirproperties and their relations.

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Outline

Knowledge vs Data



Propositional Logic

Syntax

SemanticsFirst-order Logic

Conclusion

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First-order Logic

First-order logic furnishes us with a much moreexpressive knowledge representation language thanpropositional logic

We can directly talk about objects, their properties,relations between them, etc.

Here, we will have a quick tour of first-order logic

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Syntax of First-order Logic (Predicate logic)

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Language of First-Order Logic

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Converting English into First-Order Logic

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Nested Quantifiers

The order of quantification is very important

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Semantics of First-Order Logic

An interpretation is required to give semantics to first-order logic. The truth of any formula depends on theinterpretation.

The interpretation provides, for each:

constant symbol an objectin the domain

function symbols a function from domain tuples to the domain

predicate symbol a relation over the domain (a set of tuples)

Then we define:

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A note to students

Dont worry much if you are about to getting confuse

about new terms, symbols & semantic interpretation.

We wont go deeper in details of first-order logic as it

has been introduced as an example of an analysisrepresentation technique.

However, you should know why first-order logic isbetter than propositional logic.

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Conclusion

Due to the ambiguity in natural languages there is aneed to specify knowledge through the use of formallanguages

Not only will these formal languages give us a way to

remove ambiguity but they will also help to providemethods for automating inference

Propositional logicand first-order logic is a move inthis direction for Knowledge representation and

reasoning formalism This means we can draw new conclusions from the

knowledge we have (i.e. we can reason & haveenough to build a knowledge-based agent)

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241 320 Design Architecture & Kno ledge Representation and 38

Reading

5 (Knowledge Representation)

Note:KR

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