Knowledge and Data - Canvas Quizzes Bachelor Artificial Intelligence Year 2
Module 1
Question 1: Which of the following sentences is true (at least according to Forbes)?
❏ Without sufficient data, tacit knowledge is useless in practice.
❏ The more different datasets need to be integrated, the more suitable relational databases are.
❏ The most time-consuming task of a data scientist is usually to transform relational data into
knowledge graphs.
❏ Knowledge graphs are the only way to make tacit knowledge explicit.
❏ There is usually more time spent on preparing, linking, and cleaning data than on building
the datasets in the first place.
❏ There can be no data science without knowledge graphs.
❏ The most time-consuming problem for data scientists is usually to find the right algorithm for
pattern recognition.
Question 2: Consider the following relational databases with tables Students and Studies.
Students vunetID Study follows course
Paula pas344 IK K&D
Frank fex444 IMM K&D
Studies name university language course
IMM Information, Management
and Multimedia VU Dutch K&D
IK Informatiekunde UvA Dutch Networks
Please write down a knowledge graph (in the format (s p o)) to represent the knowledge of this database
as faithfully as possible. You do not need to model the entire dataset: give 15 triples, which could include
triples that model implicit knowledge to enrich the data, e.g. about types.
(Paula, isa, student), (Frank, isa, student), (Paula, hasvunetID, pas344), (Frank, hasvunetID,
fex444), (IK, isa, study), (IMM, isa, study) (Paula, followscourse, K&D), (Paula, studies, IK),
(Frank, studies, IMM) (IK, name, "Informatiekunde"), (IMM, name, "Information, Management
and Multimedia"), (VU, isa, university), (UvA, isa, university) (Dutch, isa, language), (K&D, isa,
course), (Networks, isa, course)
,Knowledge and Data - Canvas Quizzes Bachelor Artificial Intelligence Year 2
Question 3: Consider the following formula, which is in Infix syntax:
¬((A → (¬B ∨ C)) v (¬D v ¬E))
What is an equivalent representation in Prefix syntax?
❏ ¬(v(→ (A,v(¬(B),C)),v(¬(D),¬(E))))
❏ v(¬(v(A,→(¬(B),C)),v(¬(D),¬(E))))
❏ ¬(v(→(v(v(v(¬(¬(¬(A, B,C,D,E))))))
❏ ¬(v(→ (E,v(¬(B),D)),v(¬(C),¬(A))))
❏ ((((E)¬,(D)¬)v,((C,(B)¬)v,)→)v)¬
Question 4: In Propositional Logics, which of the following entailments is true, and which is false?
(a) p → (q → r) ⊨ p → (r → q)
(b) p → (¬q ∨ r), ¬r ⊨ ¬q → ¬p
(c) q ⊨ p → q
(a) is true, (b) is true and (c) is true
(a) is false, (b) is false and (c) is true
(a) is false, (b) is false and (c) is false
(a) is true, (b) is false and (c) is true
(a) is false, (b) is true and (c) is true
Question 5: It is easy for humans to see that a formula 3*x < 12 + 6*y and y = 1 implies (or entails)
that x < 10.
Give the formal argument why this is the case according to the model theoretic semantics given in the
lecture (and thus NOT using your calculus skills!). 4 rows should suffice. Use the words assignment or
interpretation and model.
The definition is that a formula F entails G iff all models for F are models for G.
So, what are models of F? Models of F are interpretations of the variables that make F true. So, any
model for y=1 so I(y)=1 for all models I of y=1. Any interpretation I that is a model of 3*x < 12 +
6*y must therefore have the following property: 3*I(x) < 12 + 6, which implies that 3 * I(x) < 18,
which means that I(x) < 6. But then I(x) < 10, which implies that I is also a model of x<10.
, Knowledge and Data - Canvas Quizzes Bachelor Artificial Intelligence Year 2
Question 6: The task is to design a very simple new Formal System. The only thing you can say in this
language is "Oeps" and "Whow".
Define the syntax of this language L. You can either give a regular expression (not introduced in this
course), or an inductive definition (as we did with arithmetic and concept logic). This means, define a set
of basic propositions P and an inductive definition to define your language L, i.e. the set of well-formed
sentences.
You will need exactly 3 lines for this:
1) the basic propositions
2) the base-case, i.e. the most simple sentences
3) the inductive case, i.e how to construct complex sentences
There are two statements we want to make, two propositions, Oeps and Whow (I will abbreviate
them as O and W).
The base-case to define our language L, the most simple sentences are thus just O and W., so O ∈ L
and W ∈ L.
The induction is then: If a formula F∈L, then FO∈L and FW∈L. This just means that if we
concatenate O and W at the end of a well-formed Formula, we get a new wellformed formula.
Concatenation is in this case like the operators in PL (and using any operator to combine the words
O and W are of course ok to use).
Question 7: Let's continue with your simple formal systems about Oeps and Whow.
Your friends know that if you say more "Oeps" than "Whow", you are unhappy, otherwise you are happy.
Can you give a definition of the Semantics of your language, so that for any well-formed sentence, you
can determine whether you are happy or unhappy.
Here you need exactly two lines:
1) Let p ∈ P, what is the interpretation I(p)?
2) If s∈ L is a sentence, what is the interpretation of I(s)? Make use of the way you defined the language
in the previous question.
Module 1
Question 1: Which of the following sentences is true (at least according to Forbes)?
❏ Without sufficient data, tacit knowledge is useless in practice.
❏ The more different datasets need to be integrated, the more suitable relational databases are.
❏ The most time-consuming task of a data scientist is usually to transform relational data into
knowledge graphs.
❏ Knowledge graphs are the only way to make tacit knowledge explicit.
❏ There is usually more time spent on preparing, linking, and cleaning data than on building
the datasets in the first place.
❏ There can be no data science without knowledge graphs.
❏ The most time-consuming problem for data scientists is usually to find the right algorithm for
pattern recognition.
Question 2: Consider the following relational databases with tables Students and Studies.
Students vunetID Study follows course
Paula pas344 IK K&D
Frank fex444 IMM K&D
Studies name university language course
IMM Information, Management
and Multimedia VU Dutch K&D
IK Informatiekunde UvA Dutch Networks
Please write down a knowledge graph (in the format (s p o)) to represent the knowledge of this database
as faithfully as possible. You do not need to model the entire dataset: give 15 triples, which could include
triples that model implicit knowledge to enrich the data, e.g. about types.
(Paula, isa, student), (Frank, isa, student), (Paula, hasvunetID, pas344), (Frank, hasvunetID,
fex444), (IK, isa, study), (IMM, isa, study) (Paula, followscourse, K&D), (Paula, studies, IK),
(Frank, studies, IMM) (IK, name, "Informatiekunde"), (IMM, name, "Information, Management
and Multimedia"), (VU, isa, university), (UvA, isa, university) (Dutch, isa, language), (K&D, isa,
course), (Networks, isa, course)
,Knowledge and Data - Canvas Quizzes Bachelor Artificial Intelligence Year 2
Question 3: Consider the following formula, which is in Infix syntax:
¬((A → (¬B ∨ C)) v (¬D v ¬E))
What is an equivalent representation in Prefix syntax?
❏ ¬(v(→ (A,v(¬(B),C)),v(¬(D),¬(E))))
❏ v(¬(v(A,→(¬(B),C)),v(¬(D),¬(E))))
❏ ¬(v(→(v(v(v(¬(¬(¬(A, B,C,D,E))))))
❏ ¬(v(→ (E,v(¬(B),D)),v(¬(C),¬(A))))
❏ ((((E)¬,(D)¬)v,((C,(B)¬)v,)→)v)¬
Question 4: In Propositional Logics, which of the following entailments is true, and which is false?
(a) p → (q → r) ⊨ p → (r → q)
(b) p → (¬q ∨ r), ¬r ⊨ ¬q → ¬p
(c) q ⊨ p → q
(a) is true, (b) is true and (c) is true
(a) is false, (b) is false and (c) is true
(a) is false, (b) is false and (c) is false
(a) is true, (b) is false and (c) is true
(a) is false, (b) is true and (c) is true
Question 5: It is easy for humans to see that a formula 3*x < 12 + 6*y and y = 1 implies (or entails)
that x < 10.
Give the formal argument why this is the case according to the model theoretic semantics given in the
lecture (and thus NOT using your calculus skills!). 4 rows should suffice. Use the words assignment or
interpretation and model.
The definition is that a formula F entails G iff all models for F are models for G.
So, what are models of F? Models of F are interpretations of the variables that make F true. So, any
model for y=1 so I(y)=1 for all models I of y=1. Any interpretation I that is a model of 3*x < 12 +
6*y must therefore have the following property: 3*I(x) < 12 + 6, which implies that 3 * I(x) < 18,
which means that I(x) < 6. But then I(x) < 10, which implies that I is also a model of x<10.
, Knowledge and Data - Canvas Quizzes Bachelor Artificial Intelligence Year 2
Question 6: The task is to design a very simple new Formal System. The only thing you can say in this
language is "Oeps" and "Whow".
Define the syntax of this language L. You can either give a regular expression (not introduced in this
course), or an inductive definition (as we did with arithmetic and concept logic). This means, define a set
of basic propositions P and an inductive definition to define your language L, i.e. the set of well-formed
sentences.
You will need exactly 3 lines for this:
1) the basic propositions
2) the base-case, i.e. the most simple sentences
3) the inductive case, i.e how to construct complex sentences
There are two statements we want to make, two propositions, Oeps and Whow (I will abbreviate
them as O and W).
The base-case to define our language L, the most simple sentences are thus just O and W., so O ∈ L
and W ∈ L.
The induction is then: If a formula F∈L, then FO∈L and FW∈L. This just means that if we
concatenate O and W at the end of a well-formed Formula, we get a new wellformed formula.
Concatenation is in this case like the operators in PL (and using any operator to combine the words
O and W are of course ok to use).
Question 7: Let's continue with your simple formal systems about Oeps and Whow.
Your friends know that if you say more "Oeps" than "Whow", you are unhappy, otherwise you are happy.
Can you give a definition of the Semantics of your language, so that for any well-formed sentence, you
can determine whether you are happy or unhappy.
Here you need exactly two lines:
1) Let p ∈ P, what is the interpretation I(p)?
2) If s∈ L is a sentence, what is the interpretation of I(s)? Make use of the way you defined the language
in the previous question.
