Samenvatting - Skills for AI (XM_0077)

Skills for AI
Period 1 | 2022-2023

,Inhoud
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Course setup 3

Planning 4

Belangrijke symbolen 5

Logic 6
W1: Introduction & basics 6
W2: Semantic entailment 12
W3: CNF & DNF 15
W3: Advanced propositional logic 20
W4: Logic Set Theory 23
W5: First-order logic 26
W5: First-order logic applications 31
W6: First-order logic tautologies and proof 33

Linear Algebra 37
W1: Basics 37
W2: Multiplication 40
W3: Inverse 45
W4: Vectors 51
W5: Graphs 56
W6: Gradients 58
W7: Probability 62

,Course setup
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● Dr. Sieuwert van Otterloo (contact via )
● Grade computation
○ 25% Quizzes (replacement assignment)
○ 35% Assignments
■ Logic exercise 1
■ Python exercise ‘truth table’
■ W4-LinAlg-Neural Network
■ Python exercise ‘first order logic’
■ Python assignment ‘estimate gradient’
○ 40% On campus exam
● Course material
○ Logic
■ Canvas
○ Linear Algebra
■ Canvas
■ Optionally: Linear Algebra and its Applications, by David C. Lay, Steven R.
Lay and Judi J. McDonald, global edition (fifth edition), Pearson
https://home.cs.colorado.edu/~alko5368/lecturesCSCI2820/mathbook.pdf
● Chapter 1: complete chapter
● Chapter 2: 2.1, 2.2 (2.3 highly recommended)
● Chapter 3: 3.1 (recommended), 3.2
● Chapter 4: 4.2 (concept null space)
● Chapter 5: 5.1, 5.2
○ Students may wish to consult: How to Think Like a Computer Scientist, Learning with
Python, 2nd Edition, by Jeffrey Elkner, Allen B. Downey, and Chris Meyers see the
URL: https://openbookproject.net/thinkcs/python/english3e/
● Deadlines
○ 1 nov: Python assignments
○ 26 okt: Final exam

, Belangrijke symbolen
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¬ negation
∧ conjunction (and)
∨ disjunction (inclusive or; one of the two or both)
⊕ ‘either ... or...′ (exclusive or; one of the two and not both)
⇒ implication
⇔ bi-implication
φ formula (small letter phi)
ψ formula (small letter psi)
v valuation (0 or 1)
≡ semantically equivalent (identical columns in their truth tables)
⊨ semantic entailment
ℕ natural numbers, defined as the set {1, 2, 3, 4, ...)}
ℤ integers, defined as the set {..., -3, -2, -1, 0, 1, 2, 3, …}
ℚ rational numbers, defined as numbers of the form p/q where p, q ∈ ℤ and q≠0
ℝ real numbers (with √2,π,e,etc.)
ℂ complex numbers, numbers of the form a + ib where a, b ∈ R and i = √−1
{x1, …, xn} set
(x1, …, xn) n-tupel
𝚽 condition (capital letter phi; {x : 𝚽(x)})
ϕ formula (small letter phi)
ψ formula (small letter psi)
v valuation (0 or 1)