Chapter 10 - Knowledge representation

Question 1

What is this chapter about?

Answer 1

We are now interested in understanding what type of content we should add to our knowledge base.

Question 2

What is ontology?

Answer 2

Ontology is a formal representation of a set of concepts within a domain, and the relationships between those concepts.

Question 3

Complex domains require flexible and general representations. What should we concentrate on?

Answer 3

We should focus on general concepts, such as Events, Time, Physical Objects, Beliefs. These abstract concepts are present in most domains.

Question 4

Elaborate on leaving placeholders for new knowledge

Answer 4

Instead of defining everything at once, we can leave placeholders for new knowledge. For instance, we can define what it means to be a physical object, and then the finer details of specific objects can be filled in later.

There is a good analogy to object oriented programming. We create interfaces with a certain behavior, but we leave out the implementation. Also, framworks like Swing/JavaFX includes objects called WINDOW, which allows user to use this interface/abstract class as a starting point to fill out their own more detailed objects.

Question 5

What do we call the “general framework of concepts” in our AI-model/world?

Answer 5

Upper ontology. upper ontology is a framework, a structure of foundational concepts and relations acorss various domains of knowledge. They have the most general concepts at the top, and then more specific concepts below them.

Another definition is: Upper ontology is an ontology that consists of very general terms that are common across all domains.

Question 6

In an ontology (upper ontology) “diagram”, what does each link mean?

Answer 6

Each link means that the lower concept is a specialization of the concept above.

Question 7

What is the most important caveat in this topic?

Answer 7

Uncertainty. Using logic, either FOL or propositional make the world work in absolutes. This is often not the case. For instance, while it would be tempting to use the rule “Tomatoes are red”, tomatoes can indeed be yellow and orange. Therefore, is it paramount to handle these uncertainties.

Question 8

Of what use is an upper ontology?

Answer 8

It provides a generality that is useful for us.

For instance, in the Wompus world, we could use the creature “Being”. This allows the world to have different animals besides the wompus while the agent can learn things about them.

Question 9

What are the characteristics of general-purpose ontologies?

Answer 9

1) A general purpose ontology should be applicable in more or less ANY special-purpose domain

2) In any sufficiently demanding domain, different areas of knowledge must be unified, because reasoning and problem solving could involve several areas simultaneously. In other words, the ontology must be capable of bridging different areas of knowledge.

Question 10

Elaborate shortly on special-purpose vs general purpose ontologies.

Answer 10

a special-purpose ontology would only consider a specific level of knowledge. For instance, a very specific purpose ontology could consider the side effects of one particular type of medicine?

this would be useful if this was our only problem. However, we want our ontology to be general, so that it can serve multiple purposes

Question 11

Why do we want the ontology to be more general?

Answer 11

by making our ontology more general, we will enable our agent to function in more complex and interconnected systems.

Question 12

Elaborate on organization of objects into categories.

Answer 12

Vital part of knowledge representation. This is because a lot of reasoning actually happens at the category-level, and not at the specific object-level.

There are many reasons for this. Some include:
1) Mimics the way humans thinks. We are often interested in buying a nice object, rather than buying a nice, specific item.

2) Inheritance. Categories allow for inheritance of properties. Kind of like in Java.

Question 13

how can we represent categories in first-order logic?

Answer 13

Either one of two ways:

1) Objects
2) Predicates

We can use the predicate to indicate membership, like Basketball(b).

Or, we could reify and use objects. Reify is short for reification. Refers to turning a proposition into an object.
We would then use something like Basketballs, and then use a predicate to test for membership.

Question 14

What is a subcategory?

Answer 14

A subcategory means a category is a subset of another category. For instance, basketball is a subcategory of balls.

Question 15

What is a taxonomic hierarchy?

Answer 15

A taxonomic hierarchy is basically just taxonomy. Taxonomy is categorizing things based on their characteristics.

Question 16

Here are some facts about categories, open up:

Answer 16

e means membership of set

“An object is a member of a category”
BB9 ∈ Basketballs

A category is a subclass of another category
Basketballs ⊆ Balls

“All members of a category have some properties”
(x e Basketballs) => Spherical(x)

“Member of a category can be recognized by some properties”
Organge(x) AND Round(x) AND Diameter(x)=9.5 AND x e Balls => x e Basketballs

“A category as a whole has some properties”
Dogs e DomesticatedSpecies

Question 17

We also want to specify relations between categories that are not subclasses of each other. How do we do this?

Answer 17

One way is the disjoint property. Two or more categories are disjoint if they have no elements/members in common.

another way is using “Exhaustive decomposition”. We say that an exhaustive decomoposition of disjoint sets is known as a partition. This of course means that ALL MEMBERS of the original category falls in under one of the subcategories of the original/parent category. For instance, if we have a category called Vehicle, then all instances of Vehicle must be categorized as one of the subclasses of Vehicle.

Question 18

Elaborate on exhaustive decomposition

Answer 18

Exhaustive refers to applying to ALL members.
Decomposition is a type of split.

We say that an exhaustive decomoposition of disjoint sets is known as a partition. This of course means that ALL MEMBERS of the original category falls in under one of the subcategories of the original/parent category. For instance, if we have a category called Vehicle, then all instances of Vehicle must be categorized as one of the subclasses of Vehicle.

Question 19

How can we define rules for category membership=

Answer 19

We just state some. For instance, if we want a rule that tells us a certain object is a Bachelor, we can do this:

x e Bachelors <=> Unmarried(x) AND x e Adults AND x e Males

Question 20

What is the “partOf” relations?

Answer 20

the partOf relation is used to say that some object is a part of something else. For instance:

PartOf(Europe, Earth)

the PartOf relation is transitive and reflexive:

PartOf(x,x)

PartOf(y,x) AND PartOf(y,z) => PartOf(x,z)

Question 21

What do we do if we want to define composite objects with definite aprts but no particular structure?

Answer 21

We use a “bunch”.

For instance:

BunchOf({Apple1, Apple2, Apple3}) denotes the composite object with 3 apples as parts. We can then use the bunch as a normal object.

Question 22

How do we represent measurements, such as length?

Answer 22

We can use this:

Length(L1) = Inches(1.5) = Centimeters(3.81)
Diameter(Basketball12) = Inches(9.5)
ListPrice(Basketball12) = $(19)

These are called unit-functions.

Generally, they are called “Measures” or “Measurements”

Question 23

What is the most important aspect of measurements?

Answer 23

It is NOT the actual values. The actual values are often very diffcult to measure exactly.

The most important aspect, is that they can be ordered. This means, we can use “<” and “>” to indicate relative ordering.

Question 24

What is qualitative physics?

Answer 24

Qualitative physics is a subfield within AI that investigates how to reason about physical systems without detailed equations and numerical simulations.

Question 25

How can one view objects?

Answer 25

2 kinds:

1) Primitive objects
2) Composite objects

However, we usually reason at the level of rather large objects (like apples, cars etc) so that we dont need to take individual particles into account.

Question 26

Elaborate on individuation

Answer 26

Individuation is about division into distinct objects. For instance, for many objects is is easy to say “we have x amount of this object”, like “I see one dog”. However, there are many objects that dont naturally have this distinct ability. For instance, butter. What is one object of butter?

Objects that seems to defy obvious individuation is called “Stuff”.

Therefore, we have a distinction between stuff and things. Stuff is more liquid, while things are distinct.

Question 27

How to linguistics differ between stuff and things?

Answer 27

Count nouns and mass nouns.

Count nouns are things, while mass nouns are stuff.

Question 28

Elaborate on intrinsic vs extrinsic properties of things and stuff

Answer 28

Stuff are characterized by their intrinsic properties. These properties belong to the substance itself, rather than the object as a whole.

Things are characterized by their extrinsic properties. We would loose these properties by cutting the thing in 2 pieces.

Question 29

Why do we use event calculus?

Answer 29

We use event calculus to handle the aspect of time during events.

In the Wompus world, we only discussed discrete events that occured instnatly. The time to shoot was 0 etc. In real life, this is usually not the case. For instance, filling a hot tub. A very simple agent would treat it as a instant event, but would then not be able to function in the mean time.

Question 30

What are the objects of event calculus?

Answer 30

the objects of event calculus are:
1) Fluents
2) events
3) Time points

Fluents are aspects of the world that change. Such as “HaveBullet” in the game oneInTheChamber.

At(Shankar, Berkeley) is a fluent.

An event can be described like this:

E_I e Flyings AND Flyer(E_1, Shankar) AND origin(E_1, SF) AND Destination(E_1, DC)

Here above, Flyings is the category of all flying events. Like this, we can add any arbitrary information about them.

To assert that a fluent is actually true at some point in time t_1, and continuing to t_2, we use the predicate “T”.

T(At(Shankar, Berkeley), t_1, t_2)

Question 31

Give the set of predicates we use for this version of event calculus

Answer 31

T(f, t1, t2): Fluent f is true for all times between t1 and t2.

Happens(e, t1, t2): Event e starts at time t1 and ends at time t2.

Initiates(e, f, t): Event e causes fluent f to become true at time t

Terminates(e, f, t): Event e causes fluent f to cease to be true at time t.

Initiated(f, t1, t2): Fluent f become true at some point between t1 and t2

Terminated(f, t1, t2): Fluent f cease to be true at some point between t1 and t2.

t1 < t2: Time1 happens before time 2

Question 32

What is the purpose of the distinguished event “Start”?

Answer 32

Start describes the initial state by saying which fluents are true and which are false at the start time. Therefore, Start will use the predicates Initiates(e,f,t) to find out what fluents are true. It will also use Terminated to find the ones that are false.

Question 33

Elaborate on event calculus and time

Answer 33

We can talk about time points and time intervals.

Moments vs extended intervals.

Moments have zero duration.