10: Logic and Inference Rules

Question 1

Why is DL (Descriptive Logic) used in AI (Artificial Intelligence)?

Answer 1

To describe and reason about the relevant concepts of an application domain (known as terminological knowledge)

Question 2

In intelligent systems, knowledge needs to be ____, ____, and ____.

Answer 2

In intelligent systems, knowledge needs to be captured, communicated, and processed.

Question 3

Agents are ____ and have their own ontology and ____ with one another through such systems.

Answer 3

Agents are autonomous** and have their own ontology and **communicate with one another through such systems.

Question 4

On what two components are DL’s knowledge representation systems based?

Answer 4

• TBOX
• ABOX

note: T stands for terminology and A stands fo assertion

Question 5

What is the difference between “some” (∃) and “only” (∀)?

Answer 5

• “only” is about closure and closes off extra options
• “some” does not

Question 6

Assuming T is a top concept, translate the following to English:

Parent≡∃parentOf.T

Answer 6

Persons who are parents

Question 7

Assuming T is a top concept, translate the following to English:

∃parentOf.Female

Answer 7

Persons who have some daughter(s)

Question 8

Assuming T is a top concept, translate the following to English:

∀parentOf.Female

Answer 8

Those who are the parents of only daughters, if any

Question 9

Assuming T is a top concept, translate the following to English:

(∀.parentOf.Female)∩∃parent.Female

Answer 9

Those who are the parents of only daughters

Question 10

Write the DL equivalent of the following Protege statement:

ParentOf Some Female

Answer 10

∃parentOf.Female

Question 11

Write the DL equivalent of the following Protege statement:

ParentOf Only Female

Answer 11

∀parentOf.Female

Question 12

Write the DL equivalent of the following Protege statement:

hasGivenName value “Matthew”

Answer 12

∃hasGivenName. {Matthew}

Question 13

Assume you have 3 classes of Team, Player, and Position. Also, assume you have 2 properties of employs and plays:

team1 employs player1

player1 plays position1

Write a descriptive logic statement in Protege that returns the teams which have employed at least 3 players who play as striker or rightBack position.

Answer 13

Team and employs min 3 (Player and hasPosition some {striker, rightBack})

Question 14

Translate the following to a descriptive logic statement:

You have a class DogLike and you intend to state that if something runs like a Dog and smells like a Dog, then it is in DogLike class.

Answer 14

((runsLike some Dog) and (smellsLike some Dog)) SubClassOf DogLike

Question 15

In a nutshell, in a General Class Axiom, you say things about complex descriptions of entities without using any ____.

Answer 15

In a nutshell, in a General Class Axiom, you say things about complex descriptions of entities without using any naming.

Question 16

What will the Debugger prevent if you add the following statement to General Class Axiom?

Disease and (causedBy some A) SubClassOf: (hurts only B)

Answer 16

The Debugger will prevent inconsistency by not allowing a disease caused by some A to hurt somewhere outside B

Question 17

Assume three colors:

Colors:{red, white, blue}

And in the set Flower, each flower can have one or more color(s). The following DL query:

Flower and hasColor value red

does return any flower with red color but NOT every flower with ONLY red color. Even changing it to

Flower as (hasColor only {red})

does not solve the problem. Why is this?

Answer 17

Because OWL uses the open world assumption.

If we know that a flower has a red color, it does not mean that it does not have other colors, e.g. it can have other colors in the dataset.

Question 18

Logic helps in the challenging task of representing knowledge in www in a consistent and uniform manner so that it is ____ ____ to humans and ____ ____ by machines.

Answer 18

Logic helps in the challenging task of representing knowledge in www in a consistent and uniform manner so that it is easily comprehensible to humans and effectively inferable by machines.

Question 19

Descriptive Logic (DL) helps us to build ____ ____ from atomic concepts.

Answer 19

Descriptive Logic (DL) helps us to build complex concepts from atomic concepts.

Question 20

In DL, a domain can be described in terms of different classes, properties, and instances.

In this way, DL can facilitate generating answers to queries through ____ ____, improving future semantic search engines.

Answer 20

In this way, DL can facilitate generating answers to queries through logical reasoning, improving future semantic search engines.

Question 21

What is the intersection of Horn Logic and OWL called?

Answer 21

DLP (Description Logic Program)

Question 22

Fill in the blanks of the DLP diagram.

Answer 22

Question 23

What are the equivalent terms in Description Logic for the following OWL terms?

class, property, Object

Answer 23

• class = concept
• property = role
• Object = individual

Question 24

What is the importance of logic?

Answer 24

• high-level language for expressing knowledge
• high expressive power
• well-understood formal semantics
• precise notion of logical consequence
• proof systems that can automatically derive statements syntactically from a set of premises

Question 25

The languages of RDF and OWL can be viewed as ____ of predicate logic (first order logic).

Answer 25

The languages of RDF and OWL can be viewed as specializations of predicate logic (first order logic).

Question 26

Predicate logic and its special cases are ____, in the sense that, if a conclusion can be drawn, it remains valid even if new knowledge becomes available.

Answer 26

Predicate logic and its special cases are monotonic, in the sense that, if a conclusion can be drawn, it remains valid even if new knowledge becomes available.

Question 27

How is a rule represented in Horn Logic?

Answer 27

A1, …, A_n -> B

Question 28

Deductive Rules

(Horn Logic)

Answer 28

If A1, …, A_n are known to be true, then B is also true

Question 29

Reactive Rules

(Horn Logic)

Answer 29

If the conditions A1, …, A_n are true, then carry out the action B

Question 30

Description Logic vs Horn Logic

Answer 30

• Neither of them is a subset of the other
• Impossible to assert that a person X who is a brother of Y is uncle of Z (where Z is child of Y) in OWL
  
  • But using rules, it can be represented as brother(X, Y), childOf (Z, Y) -> uncle (X, Z)
• ​On the other hand, rules cannot assert the information that a person is either a man or a woman
  
  • In OWL, this can be expressed using a disjoint union

Question 31

Give an example of a chain of properties using circle notation.

Answer 31

• hasGrandParent is a chain of properties of hasParent o hasParent
• hasSibling is a chain of properties of hasParent o hasChild

Question 32

Assuming you have hasParent, hasSister, hasSibling, hasBrother, and hasChild properties, build the concept of a cousin based on the chain of properties through defining hasCousin.

Answer 32

hasCousin is a chain of properties of

hasParent o hasSibling o hasChild

Question 33

Give a monotonic and a non-monotonic rule for the following:

An online vendor wants to give a special discount if it is a customer’s birthday.

Answer 33

• Monotonic: If birthday, then special discount
• Non-monotonic: If birthday is not known, then not special discount
  
  • Applicable when available information is incomplete

Question 34

The Semantic Web approach is to express the knowledge in a ____ way using one of the Web languages already discussed.

Answer 34

The Semantic Web approach is to express the knowledge in a machine-accessible way using one of the Web languages already discussed.