KR Module Exam

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1

What is knowledge representation?

branch of AI concerned with the techniques for representing and reasoning about knowledge.

2

What is the long term goal of KR?

Make programs, systems, interfaces and agents behave intelligently.

3

What are the characteristics of intelligent entities?

They can reason, make decisions/plans, learn, communicate, take commands/queries/requests/preferences, act/return answers/plans/decisions/control commands

4

What is reasoning?

The process of making inferences. Make implicit knowledge explicit, correctness, and completeness

5

What do we need to reason with

Knowledge

6

How can a reasoning task be expressed?

Knowledge base to conclusion or asserted knowledge to inferred knowledge

7

How is entailment or inference defined?

Based on the concept of implication. Premise to conclusion, if ==>then, sometimes called rule.

 All men are mortal
 If something is a man, then it is mortal
 If something is not mortal, then it can't be a man
 If something is not a man, then ???

It is not mortal

8

What is deduction? Provide an example

Premise to conclusion

Socrates is a man. All men are mortal.
So, Socrates must be mortal, too

9

What is abduction? Provide an example

Conclusion to premise

All men are mortal. Socrates is mortal.
So, (it's possible that) Socrates is a man

10

What is induction? Provide an example

Premise/conclusion to implication

11

Socrates is a man and is mortal.
Aristoteles is a man and is mortal.

So, (it's likely that) all men are mortal

What are some KB search strategies?

12

Forward/Backward Chaining

What is forward chaining

13

-Start from known facts
– Make inferences to derive new facts
– Stop when goal has been derived

What is backward chaining

14

-Start from goal
– See under which premises the goal can be entailed
– Replace goal with premises
– Stop when current goal is a known fact

How is knowledge encoded in a suitable format

15

Persist

Exchange

Aquire

Reason

In declarativeness, what is how?

16

Exact step by step instructions

In declarativeness what is what

17

A high level directive or request whose detailed implementation is left up to the intelligent entity.

The more ____ level the directives and requests an entity can handle, the more ____ it is

18

High, intelligent

What is appropriate knowledge representation

19

can be consumed by a “standard” reasoning process
“Implemented” by an “intelligent” being

What is language

20

Syntax and Semantics

What is the fundamental issue of KR

21

Need appropriate languages to be able to
express
 Knowledge
 Queries
 Preferences
 High-level directives

Given KB to conclusion, we need

22

Syntax
– (how to write) KB and Conclusion.
• Semantics
– (meaning) for ‘’.
– Semantics ~ “Enumerating the ‘models’ of KB”

What should KB be?

23

Incremental, should be easy to add and revise knowledge.

What is (non) monotonicity

24

KB ==> Conclusion
 KB + New Knowledge==> not Conclusion

Provide an example of default language

25

I don't know this, but given that normally this...

Provide an example of episthemic language

26

I believe that you know this

Provide an example of modal language

27

This is possibly while that is necessarily

Provide an example of deontic language

28

This is obligatory, while that is prohibited

Provide an example of defeasible language

29

This would be true except that

Provide an example of temporal language

30

This is true now

Rule Based Inference example

31

Inclusion: gender, female, pregnant, gestational age...

Exclusion: chorioamnionitis, non-reasuring fetal testing

ancestor(X,Y)  ancestor(X,Z), parent(Z,Y).
ancestor(X,Y)  parent(X,Y).
parent( alex, bob ).
parent( bob, carlos ).
parent( bob, diana ).
parent( fiona, alex ).
Can you derive the full ancestry knowledge inherent here
(ie, all the facts that can be derived from the given facts)?

What must we do in KR (need a way to write? assign meaning to?)

32

We need a way to write (syntax) and assign meaning to
(semantics):
– Facts (previous knowledge)
– Rules (conditions) + allow learning
– Questions (queries)
– Goals
so a computer can process them and reach reasonable
conclusions (answers, plans, new knowledge).

Applications of reasoning?

33

Reasoning with incomplete information, default
reasoning.
– Reasoning with preferences and priorities, inheritance
hierarchies.

What is featured in declarative problem solving

34

Planning, job shift scheduling.
– Explanation generation, diagnosis.
– Combinatorial graph problems.

Further applications of KR

35

Causal modeling, medical decision support systems

What is of fundamental importance in building intelligent entities

36

Representing knowledge and reasoning with it is of fundamental importance in
building intelligent entities.

What are specific languages used for in KR

37

Specific languages are used to express (represent) this knowledge and infer new
knowledge from it (reason).

What are logics

38

formal languages for representing information such that conclusions can be drawn

What is syntax

39

defines the sentences in the language

What are semantics

40

define the "meaning" of sentences

What is a model

41

“worlds” with respect to which truth can be evaluated

What is entailment

42

expresses the notion that a sentence logically follows (can be derived from) another. Used to carry out logical inference.

What is logical inference

43

the process derivation of all sentences that logically follow another

What are the two parts of interpretation

44

Domain and interpretation mapping

What is the domain of discourse

45

can be any non-empty set, not just formal/mathematical object (i.e. people, tables, numbers, unicorns, chunks of PB, the universe)

What is an interpretation mapping

46

If P is a predicate symbol of arity, an n-aray relation over D for propositional symbols....etc...

What are the assumptions of first order logic

47

Assumes the world contains objects, relations, and functions

What are objects

48

Protein, people, house, numbers

What are relations

49

activates, red, round, prime,
brother, part of, comes between, … any
assertion of the form R(x),

What are functions

50

>, <, one more than, plus, … any
f(x) applied to an object x (or a set of objects).

Basic elements of first order logic

51

Constants: john, 2, asu,...
• Predicates: brother, active,...
• Functions: sqrt, leftLegOf,...
• Variables: X, Y, A, B, Test, …
• Connectives: Ø, Þ , Ù, Ú, Û
• Equality: =
• Quantifiers: ", $

What is an atomic sentece

52

Atomic sentence
: predicate (term1,...,termn)
| term1 = term2

where a term is defined as follows:
Term
: function (term1,...,termn)
| constant
| variable

What are complex sentences. Provide an example

53

Complex sentences are made from atomic
sentences using connectives

ØS, S1 Ù S2, S1 Ú S2, S1 Þ S2, S1 Û S2,

E.g.
– Sibling(x,y) Þ Sibling(y,x)
– greater(x,y) Ú lessOrEqual(x,y)
– >(x,y) Ù Ø >(x,y)

When are sentences true

54

Sentences are true with respect to a model and an
interpretation

What does a model contain

55

A model contains objects (domain elements) and
relations among them

What does an interpretation specify referent for

56

constant symbols → objects
predicate symbols → relations
function symbols → functional relation

When is an atomic sentence predicate true

57

An atomic sentence predicate(term1,...,termn) is true
if the objects referred to by term1,...,termn
are in the relation referred to by predicate

What are complex sentences

58

truth functional

What are complex sentences based on

59

Based on the truth value of each atom
– Combined using the operators' “truth tables”
OR y Øy
x T T
Øx T F

AND y Øy
x T F
Øx F F

Write universal quantification for: Everyone at ASU is smart

60

"vX : at(X,asu) → smart(X)

Vx what is stand for

61

P is true in a model m iff P is true for all possible
objects x in the model

Roughly speaking, equivalent to the conjunction of
instantiations of P

62

at(jian,asu) → smart(jian)
Ù at(richard,asu) → smart(richard)
Ù at(asu,asu) → smart(asu)
Ù at(abc129,asu) → smart(abc129)

Typically, ==> is the main connective used

63

V

Common mistake: using ^ as the main
connective with?

64

V

VX: at(X,asu) ^ Smart(X) means?

65

“Everyone is at ASU and everyone is smart”

Existential quantification for: Someone at ASU is smart:

66

EX: at(X,asu) ^Smart(X)

Ex P is true in a model m if

67

P is true with x being some possible object (at least one) in the model

Existential quantification is equivalent to?

68

Roughly speaking, equivalent to the disjunction of
instantiations of P

Vx Vy is the same as

69

Vy Vx

Ex Ey is the same as

70

Ey Ex

Ex Vy is not the same as

71

Vy Ex

Ex Vy loves(X,Y) stands for

72

There is a person who loves everyone in the world”

Vy Ex loves(X,Y)

73

“Everyone in the world is loved by at least one person”

What is a quantifier duality

74

each can be expressed using the other

Two sentences are logically equivalent if

75

true in same model

term1 = term2 is true under

76

a given interpretation if and only if term1 and term2 refer to the same object

John is Mark's brother

77

brother(john, mark)

John has a brother

78

brother( john, theBrotherOf(john) )
– or -
EX : brother(john, X)

John is a man

79

man(john)
– or –
isA(john, man)

VX,Y: brother(X,Y) ==> Sibling(X,Y)

80

Brothers are siblings

VM,C mother(C) = M <==>
(female(M) ^ Parent(M,C))

81

One's mother is one's female parent

“Sibling” is symmetric

82

VX,Y: Sibling(X,Y) <==> Sibling(Y,X)

Definition of Sibling in terms of Parent:

83

VX,Y : sibling(X,Y)
“Any two individuals are siblings iff”

John is a patient

84

patient( john )

John suffers from diabetes

85

suffersFrom( john, diabetes )

John is taking some drug for diabetes

86

E D: drug(D) ^ takes(john, D) ^ treats(D, diabetes)

(All) drugs treat some disease

87

VD: drug(D) ==> E X : disease(X) ^ treats(D,X)

(All) drugs treat (all) diseases

88

VD,X: drug(D) ^ disease(X) ==> treats(D,X)

Try defining “uncle” and “aunt”
in terms of “brother” / “sister” and “parent

89

VX,Y : uncle(X,Y)
<==>
EF: parent(F,Y) ^ brother(X,F)
• VX,Y : uncle(X,Y)
<==>
EF,G :
parent(F,Y)
^parent(G,F)
^ parent(G,X)
^ Ø (X = F)

What can first order logic represent

90

FOL can represent knowledge about a simple
domain

What can logical reasoning do

91

Logical reasoning can discover new facts using
inference

...