KR LEVEL

Question 1

Perceiving, thinking, acting – what did we set
out to learn in this lecture?

Answer 1

Perceive
We didn‘t talk about this yet: Data and natural language as input
to artificial intelligence-enabled systems, or artificial intelligence
analytics methods
Think
Rules, logic, graphs: Different knowledge representations and
reasoning mechanism
We didn’t talk about this yet: machine learning.
Act
This comes up very indirectly throughout this course, in the sense
that system/algorithm output informs human users or is consumed
by other systems.

Question 2

Knowledge Representation

Answer 2

Express and differentiate between:
▪ Facts (assertional axioms - logic, graphs)
▪ General knowledge (rules; terminological axioms – predicate
logic,graphs)

Question 3

Reasoning

Answer 3

Logic, graph-based procedures: Infer new knowledge, check for
the correctness of specific statements, can find related entities
(spreading activation, shortest path), and characterize entities
with different graph measures

Question 4

Learning

Answer 4

(no learning yet)

Question 5

Problems with knowledge representations
from symbolic AI

Answer 5

Symbolic AI – relies on expressing knowledge in terms of human-readable, high-level
symbolic expressions and concepts – in our lecture: rules, logic, and semantic
networks

Question 6

Suitability to real-world problems:

Answer 6

: It is difficult to describe complex
entities in logic-based, symbolic KR formalisms (graph representations
help to some degree)

Question 7

Modelling effort:

Answer 7

Symbolic knowledge representations are typically
manually engineered (rules, object-oriented KR, knowledge graphs)
➢ Vocabulary and formal KR needs to be modelled, is difficult to
derive automatically (loosening requirements on formality helps)

➢ Suitable for metadata and common characteristics (attributes,
properties, …)
➢ Suitable if formal description is sufficiently important – e.g., formal
verification of important systems.

Question 8

Reasoning:

Answer 8

New inferences, validation, consistency checking.
Scalability and decidability can be an issue.

Question 9

Representation

Answer 9

Goal: Computationally
represent books, e.g., Harry
Potter and the Half-Blood
Prince.
Definition: A representation
Y conforms in a systematic
manner to X , preserving
pre-selected characteristics
of X.
A representation always
loses something, it is an
approximation.

Question 10

Represent this book in predicate logic:

Answer 10

Book(Harry-potter-hbp).
▪ hasCoverColor(Harry-potter-hbp, green)
▪ isGenre(Harry-potter-hbp, fantasy-novel)
▪ isGenre(Harry-potter-hbp, young-adult-novel)
▪ …
▪ Fictional-Character(Harry)
▪ Fictional-Character(Hermione)
▪ Fictional-Character(Ron).
▪ appearsIn(Harry,Harry-potter-hbp)
▪ …
▪ is-friend-of(Harry,Hermione)
▪ is-friend-of(Harry,Ron)
▪ ..

Question 11

How suitable is predicate logic as a
knowledge representation formalism
to represent books?

Answer 11

+ Suitable for expressing meta-data, and
describing characteristics of the book that
are similar across books – facts and
knowledge ABOUT the book
▪ Imagine expressing the complete story of
Harry Potter in predicate logic!
▪ Yahoo! initially categorised web sites in a
web directory – required editors
~ Metadata could be extracted from a digital
version of the book with some heuristics, if
reasonable metadata schema exists a
priori (-> typical research/engineering goal
in NLP „fact extraction“, „slot filling“,
„named entity recognition“)

Question 12

Idea: Vectors as numeric, non-symbolic
representation of complex entities

Answer 12

From items to vectors, and how to reason
using vectors
1. Choose knowledge representation (KR) formalism:
Vectors
2. Choose how to represent items into vectors (~feature
engineering).
▪ Choose relevant characteristics of the item!
KR perspective: An entity has a set of characteristics; in
machine learning these correspond approximately to
„features“; in statistics the term „variables“ is more typical.
▪ Choose easily computable characteristics of the item!
▪ …which are representable as real numbers.
3. Choose operations on the represented items
▪ Vector mathematics has a broad range of operations –
identify what do they mean in a given use case, and which
are useful

Question 13

Choosing operations on vectors for reasoning
- What questions do we want to ask?

Answer 13

For a given entity:
▪ What are similar entities?
▪ To which groups does an entity belong? (classification)
▪ What will we be able to observe about this entity in the future? (prediction)
Over a set of entities:
▪ What are meaningful sub-groups? (clustering)
▪ Is there a correlation between different entity characteristics?
▪ Does one characteristic cause another one? (attention – typically needs
specific study set-up to assert!)
▪ Is there a more compact representation – which variables carry most
information? (factor analysis)

Question 13

Why is similarity interesting?

Answer 13

Recommendation: If you like book A, and book B is
similar to A, then you will probably also like book B.
▪ Information retrieval: If your question (query) is q,
then the answer to your question (a document) should
be similar to q.
▪ Classification: All members of a class are similar
w.r.t. to specific features
▪ Clustering: Build groups of entities that are more
similar to each other than they are to members of
other groups

Question 14

Vector Representations in this lecture

Answer 14

In this lecture, we will
▪ Compute similarities (today)
▪ Application example: information retrieval and
how to „translate“ natural language into vectors
(next lecture)
▪ Classification and clustering

Question 15

Discussion: Using vectors to represent
complex entities…

Answer 15

Allows us to use everything from simple to complex
functions to compute single entries in the vector
(„features“).
▪ Allows us to use vector mathematics as a way to reason
over knowledge
▪ Complex operations on vectors available – including the
whole field of statistics!
▪ Feature engineering is still knowledge-intensive…
▪ … but if easily computable features are chosen, once the
features are chosen, the representation of a concrete
entity is easy (typical: choose a representation that can be
created automatically)

Question 16

Is it a new way to structure knowledge, or is it
a data structure?

Answer 16

A single vector represents a data “point”, an instance
▪ The choice of which entities are represented is a
knowledge engineering choice
▪ … as is the choice of how to represent every single
instance
▪ sometimes called “feature set”, or “dictionary vector” in
information retrieval
▪ Underlying assumption: We can represent a complex
entity as a finite set of numbers.
➢We give up the capability to express general knowledge
formally – the general knowledge is hidden in the choice of
which entities to represent and in the choice of features.

Question 17

How similar are two entities?

Answer 17

What are characteristics for comparison?
-> Choice in representation

Harry Potter - Bible

How similar are two entities when they are
represented as vectors?

Cosine similarity – a widely used measure of
similarity between two vectors

Cosine similarity – values it takes
Values are between [-1;1]
▪ Angle is 0°=> Cos(0°)=1
▪ Vectors have the same direction, and are maximally
similar. Cosine doesn’t measure vector equality!!!
▪ Angle is 90 °=> Cos(90°)=0
▪ Vectors are orthogonal; they are not similar at all.
▪ Angle is 180°=> Cos(180°)=-1
▪ Vectors show into the opposite direction, they are
inverse.

Question 18

Cosine similarity - formula

Answer 18

▪ Independent of the lengths (magnitude) – normalizes
vectors.
▪ Measures direction

sim(a,b) = cos(theta) =

   a * b \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ ||a|| * ||b||