Summary
L1 — Introduction
One relevant part of human intelligence:
Depends on explicitly known facts we have learned or can access.
Derives implicit knowledge through reasoning.
Can be (mostly) justified based on the above two.
In AI, this part corresponds to symbolic AI, an important part of which is
Knowledge Representation.
This is not all of human intelligence; we also have intuitions. Similarly, symbolic
AI an KR are not all there is in AI.
Two Types of Intelligence
These systems correspond to two fundamentally different branches of AI:
Data-Centric/Statistical AI:
Machine Learning
Deep Neural Networks
Large Language Models
Symbolic AI:
Logical reasoning
Explicit knowledge
Transparent inferencing
… with different applications
Data-Centric/Statistical AI:
Summary 1
, Patterns recognition
Motor skils
Text/image generation
Symbolic AI:
Planning
Reasoning
Search engines
Strengths and Weaknesses
1. Construction of Knowledge
2. Scalability
3. Explainability and Trust
a. Data-centric: danger of hallucinations, explaining results are often
challenging
b. KR: proven correctness guarantees, explainable by design.
c. However: only as good as the provided knowledge
Which Approach to Choose?
Different types of AI are used for different purposed
Use KR if:
You have the knowledge
You have the resources to formalise it
You need trust, transparency and precision
The future are combined systems (e.g. neuro-symbolic AI)
KR to inform data-driven systems
data-driven to inform KR
KR to explain and verify output of data-drive systems
Summary 2
, Automated reasoning can be used to infer implicit information
L2 — Propositional Logic I
The Knowledge Base
In propositional logic, a knowledge base can have simple statements, and
complex statements.
A simple statement (proposition) states facts about the world.
In our examples we often just use a single letter for a simple statement
as variables.
Examples: p, q, r
Note: in propositional logic one traditionally calls a Knowledge Base a
“sentence”
(s → t) ≡ (¬s ∨ t)
(s ∧ t) ≡ ¬(¬s ∨ ¬t)
Defining the Semantics of a Language
Assign values to the basic building blocks of the language, the atoms.
Remember {A, B, C}is in LA , e.g. I(A)
= 1, I(B) = 2, I(C) = 3
Define how to assign values for complex sentences from other (simple or
complex) formulas
Suppose I(F )is a values for F in LA , then I(A + F
+ A) = I(A) ∗
I(F ) ∗ I(A)
Suppose I(F )is a values for F in LA , then I(B + F
+ B) = I(B) ∗
I(F ) ∗ I(B)
Suppose I(F )is a values for F in LA , then I(B + F
+ B) = I(C) ∗
I(F ) ∗ I(C)
Summary 3
, What is the value I(A + B + C + B + A)?
= I(A) ∗ I(B) ∗ I(C) ∗ I(B) ∗ I(A)
Meaning of Simple Statements
In propositional logic, the meaning of a statement is either true or false.
We call this the “interpretation function” I :
It maps any statement pto true or false:
I(p) = 0or I(p) = 1
Special Statements
Tautologies
Statements, which are true in any world that we can possibly images, are called
tautologies or valid.
(a ∨ ¬a)
Inconsistencies
There are also statements which are always false. They are false in every world
we can possibly imagine. Such statements are called inconsistent.
(a ∨ b) ∧ (¬a ∧ ¬b)
Satisfiable
Statements which are not a tautology nor inconsistent —they are always for
some combination of truth-values and false for other— are called satisfiable.
(a ∨ b) ∧ (¬a ∨ ¬b)
Terms
Summary 4
L1 — Introduction
One relevant part of human intelligence:
Depends on explicitly known facts we have learned or can access.
Derives implicit knowledge through reasoning.
Can be (mostly) justified based on the above two.
In AI, this part corresponds to symbolic AI, an important part of which is
Knowledge Representation.
This is not all of human intelligence; we also have intuitions. Similarly, symbolic
AI an KR are not all there is in AI.
Two Types of Intelligence
These systems correspond to two fundamentally different branches of AI:
Data-Centric/Statistical AI:
Machine Learning
Deep Neural Networks
Large Language Models
Symbolic AI:
Logical reasoning
Explicit knowledge
Transparent inferencing
… with different applications
Data-Centric/Statistical AI:
Summary 1
, Patterns recognition
Motor skils
Text/image generation
Symbolic AI:
Planning
Reasoning
Search engines
Strengths and Weaknesses
1. Construction of Knowledge
2. Scalability
3. Explainability and Trust
a. Data-centric: danger of hallucinations, explaining results are often
challenging
b. KR: proven correctness guarantees, explainable by design.
c. However: only as good as the provided knowledge
Which Approach to Choose?
Different types of AI are used for different purposed
Use KR if:
You have the knowledge
You have the resources to formalise it
You need trust, transparency and precision
The future are combined systems (e.g. neuro-symbolic AI)
KR to inform data-driven systems
data-driven to inform KR
KR to explain and verify output of data-drive systems
Summary 2
, Automated reasoning can be used to infer implicit information
L2 — Propositional Logic I
The Knowledge Base
In propositional logic, a knowledge base can have simple statements, and
complex statements.
A simple statement (proposition) states facts about the world.
In our examples we often just use a single letter for a simple statement
as variables.
Examples: p, q, r
Note: in propositional logic one traditionally calls a Knowledge Base a
“sentence”
(s → t) ≡ (¬s ∨ t)
(s ∧ t) ≡ ¬(¬s ∨ ¬t)
Defining the Semantics of a Language
Assign values to the basic building blocks of the language, the atoms.
Remember {A, B, C}is in LA , e.g. I(A)
= 1, I(B) = 2, I(C) = 3
Define how to assign values for complex sentences from other (simple or
complex) formulas
Suppose I(F )is a values for F in LA , then I(A + F
+ A) = I(A) ∗
I(F ) ∗ I(A)
Suppose I(F )is a values for F in LA , then I(B + F
+ B) = I(B) ∗
I(F ) ∗ I(B)
Suppose I(F )is a values for F in LA , then I(B + F
+ B) = I(C) ∗
I(F ) ∗ I(C)
Summary 3
, What is the value I(A + B + C + B + A)?
= I(A) ∗ I(B) ∗ I(C) ∗ I(B) ∗ I(A)
Meaning of Simple Statements
In propositional logic, the meaning of a statement is either true or false.
We call this the “interpretation function” I :
It maps any statement pto true or false:
I(p) = 0or I(p) = 1
Special Statements
Tautologies
Statements, which are true in any world that we can possibly images, are called
tautologies or valid.
(a ∨ ¬a)
Inconsistencies
There are also statements which are always false. They are false in every world
we can possibly imagine. Such statements are called inconsistent.
(a ∨ b) ∧ (¬a ∧ ¬b)
Satisfiable
Statements which are not a tautology nor inconsistent —they are always for
some combination of truth-values and false for other— are called satisfiable.
(a ∨ b) ∧ (¬a ∨ ¬b)
Terms
Summary 4
