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Question 1 of 60
Quiz ID: q1
What is the primary ontological commitment of First-Order Logic (FOL) that distinguishes it from propositional logic?
Facts that either hold or do not hold
Objects in the world and relations among them
Facts that hold at particular times
Degree of belief in facts
Question 2 of 60
Quiz ID: q2
Which of the following is an example of a unary relation in FOL?
Married(John, Mary)
LargerThan(3, 2)
Round(Ball)
LeftLeg(John)
Question 3 of 60
Quiz ID: q3
In FOL, what does the epistemological commitment regarding a fact allow?
It defines what exists in the world
It specifies the possible states of knowledge an agent can have about a fact
It determines the syntactic structure of a sentence
It assigns a degree of truth to a fact
Question 4 of 60
Quiz ID: q4
According to the provided table, which language has an ontological commitment that includes 'facts with degree of truth'?
Propositional logic
First-order logic
Temporal logic
Fuzzy logic
Question 5 of 60
Quiz ID: q5
In a model for FOL, what is a 'domain'?
The set of all possible interpretations for symbols
The set of objects the model contains
The set of all valid sentences in the knowledge base
The set of functions that are total
Question 6 of 60
Quiz ID: q6
What is the role of an 'intended interpretation' in FOL?
To define the syntax of well-formed formulas
To list all possible models for a set of sentences
To specify which object, relation, or function a symbol refers to
To determine the truth value of a quantified sentence
Question 7 of 60
Quiz ID: q7
Which of the following is NOT a basic syntactic element of FOL?
Constants
Predicates
Probabilities
Quantifiers
Question 8 of 60
Quiz ID: q8
What is a 'Term' in FOL?
A logical expression that refers to a truth value
A logical expression that refers to an object
A predicate followed by a list of arguments
A sentence formed using a quantifier
Question 9 of 60
Quiz ID: q9
Which of these is an example of an atomic sentence?
Brother(Richard, John) ∧ King(John)
∀x (Person(x) ⇒ Mortal(x))
Brother(LeftLeg(Richard), John)
¬King(Richard)
Question 10 of 60
Quiz ID: q10
What is the primary purpose of quantifiers in FOL?
To connect two atomic sentences with a logical operator
To express properties of collections of objects without enumerating them
To define the scope of a variable within a function
To assign a specific object to a constant symbol
Question 11 of 60
Quiz ID: q11
How is the universal quantification '∀x At(x, UoM) ⇒ Smart(x)' correctly interpreted?
Everyone is at UoM and everyone is smart
If someone is at UoM, then they are smart
For every object x, if x is at UoM, then x is smart
There exists an object x that is at UoM and is smart
Question 12 of 60
Quiz ID: q12
What is the common mistake when using the universal quantifier?
Using ∧ as the main connective instead of ⇒
Using ⇒ as the main connective instead of ∧
Forgetting to specify the domain of quantification
Using a constant symbol instead of a variable
Question 13 of 60
Quiz ID: q13
How is the existential quantification '∃x At(x, UoM) ∧ Smart(x)' correctly interpreted?
Everyone at UoM is smart
There exists someone who, if they are at UoM, then they are smart
There exists an object x such that x is at UoM and x is smart
Not everyone at UoM is smart
Question 14 of 60
Quiz ID: q14
Why is '∃x At(x, UoM) ⇒ Smart(x)' a potentially problematic sentence?
It is true only if everyone at UoM is smart
It is false if no one is at UoM
It is true even if there exists someone not at UoM
It uses the wrong quantifier for the intended meaning
Question 15 of 60
Quiz ID: q15
Which of the following statements about quantifier order is TRUE?
∀x ∃y is logically equivalent to ∃y ∀x
∃x ∀y is logically equivalent to ∀y ∃x
The order of identical quantifiers (∀x∀y or ∃x∃y) can be swapped without changing meaning
The order of mixed quantifiers (∀x∃y) can be swapped without changing meaning
Question 16 of 60
Quiz ID: q16
What is the meaning of '∃x ∀y Loves(x,y)'?
Everyone loves everyone
There is someone who is loved by everyone
There is someone who loves everyone
Everyone is loved by someone
Question 17 of 60
Quiz ID: q17
What is the meaning of '∀y ∃x Loves(x,y)'?
Everyone loves everyone
There is someone who is loved by everyone
There is someone who loves everyone
Everyone is loved by someone
Question 18 of 60
Quiz ID: q18
According to De Morgan's rules for quantifiers, which is equivalent to ¬∀x P?
∀x ¬P
∃x ¬P
¬∃x P
∃x P
Question 19 of 60
Quiz ID: q19
Which of the following correctly expresses that everyone likes ice cream using an existential quantifier and negation?
∃x ¬Likes(x, IceCream)
¬∃x Likes(x, IceCream)
¬∃x ¬Likes(x, IceCream)
∃x Likes(x, IceCream)
Question 20 of 60
Quiz ID: q20
In FOL, when is the equality statement 'term1 = term2' true?
When the terms have the same syntactic structure
When the terms are both constants
When the terms refer to the same object under the given interpretation
When the terms are both variables
Question 21 of 60
Quiz ID: q21
How might FOL's equality be used to define that two people are siblings?
Sibling(x,y) ⇔ Parent(x) = Parent(y)
Sibling(x,y) ⇔ ∃p (Parent(p,x) ∧ Parent(p,y))
Sibling(x,y) ⇔ ∃p (Parent(p,x) ∧ Parent(p,y) ∧ ¬(x=y))
Sibling(x,y) ⇔ Child(x,p) = Child(y,p)
Question 22 of 60
Quiz ID: q22
In the context of a Knowledge Base (KB), what is the purpose of the TELL operation?
To ask a question and get a yes/no answer
To ask a quantified question and get a substitution
To add a new sentence to the KB
To check the consistency of the KB
Question 23 of 60
Quiz ID: q23
What does ASK(KB, ∃x Person(x)) typically return?
True or False
A substitution (binding list) for x that makes Person(x) true
A list of all objects that are persons
The number of persons in the knowledge base
Question 24 of 60
Quiz ID: q24
In the royal kinship domain, which predicate would most likely be a unary predicate?
Parent
Spouse
Male
Grandparent
Question 25 of 60
Quiz ID: q25
What is the purpose of an 'axiom' in a knowledge base?
To serve as a query asked of the KB
To provide basic factual information from which conclusions can be derived
To define the syntactic rules of the logic
To interpret the meaning of constant symbols
Question 26 of 60
Quiz ID: q26
Which axiom correctly defines a mother?
∀m, c Mother(c) = m ⇔ Parent(m, c)
∀m, c Mother(c) = m ⇔ Female(m)
∀m, c Mother(c) = m ⇔ Female(m) ∧ Parent(m, c)
∀m, c Mother(c) = m ⇔ Female(m) ∨ Parent(m, c)
Question 27 of 60
Quiz ID: q27
The axiom ∀p, c Parent(p, c) ⇔ Child(c, p) illustrates what kind of relationship?
A symmetric relationship
A transitive relationship
An inverse relationship
A reflexive relationship
Question 28 of 60
Quiz ID: q28
What is a 'theorem' in the context of a logical knowledge base?
An intended interpretation for a symbol
A sentence that is added to the KB using TELL
A sentence that is entailed by the axioms
A query asked using ASK
Question 29 of 60
Quiz ID: q29
Which of the following is likely a theorem derived from other axioms about siblings?
Male(Harry)
∀x Male(x) ⇔ ¬Female(x)
∀x, y Sibling(x, y) ⇔ Sibling(y, x)
Parent(Charles, William)
Question 30 of 60
Quiz ID: q30
What is a key expressive advantage of FOL over propositional logic?
FOL can represent degrees of belief
FOL can represent facts that change over time
FOL allows objects and relations as semantic primitives
FOL can handle uncertainty
Question 31 of 60
Quiz ID: q31
Which symbol in FOL is used to represent a specific, named object?
Predicate symbol
Function symbol
Constant symbol
Variable
Question 32 of 60
Quiz ID: q32
What does a function symbol in FOL refer to?
A relation between objects
A truth value
A logical connective
A mapping from objects to an object
Question 33 of 60
Quiz ID: q33
In the sentence Married(Father(Richard), Mother(John)), what is 'Father(Richard)'?
A constant symbol
A predicate symbol
A function term
A variable
Question 34 of 60
Quiz ID: q34
Which connective is most commonly the main connective in a universally quantified sentence?
Conjunction (∧)
Disjunction (∨)
Implication (⇒)
Biconditional (⇔)
Question 35 of 60
Quiz ID: q35
Which connective is most commonly the main connective in an existentially quantified sentence?
Conjunction (∧)
Disjunction (∨)
Implication (⇒)
Biconditional (⇔)
Question 36 of 60
Quiz ID: q36
The sentence ∀x (Cat(x) ⇒ (∃y (Mouse(y) ∧ Hates(x, y)))) translates to:
All cats hate all mice
There is a mouse that all cats hate
Every cat hates some mouse
Some cat hates every mouse
Question 37 of 60
Quiz ID: q37
What is the scope of a quantifier?
The set of all constant symbols in the knowledge base
The part of the sentence to which the quantifier applies
The domain of objects in the model
The interpretation of a function symbol
Question 38 of 60
Quiz ID: q38
A variable in a sentence is 'bound' if it:
Is a constant symbol
Is within the scope of a quantifier for that variable
Is not used in any predicate
Refers to a specific object in the domain
Question 39 of 60
Quiz ID: q39
A 'sentence' in FOL is a well-formed formula that has:
No constant symbols
At least one function symbol
No free variables
Only unary predicates
Question 40 of 60
Quiz ID: q40
Which rule of inference is often associated with the universal quantifier?
Existential Instantiation
Universal Generalization
Universal Instantiation
Existential Generalization
Question 41 of 60
Quiz ID: q41
The process of replacing a universally quantified variable with a specific object is called:
Generalization
Skolemization
Instantiation
Unification
Question 42 of 60
Quiz ID: q42
Which of these is NOT a standard binary connective in FOL?
∧ (Conjunction)
∨ (Disjunction)
¬ (Negation)
⇒ (Implication)
Question 43 of 60
Quiz ID: q43
The knowledge base contains: ∀x (Student(x) ⇒ Study(x)). We TELL it Student(Alice). What can we infer?
Study(Alice)
¬Study(Alice)
∀x Study(x)
∃x Study(x)
Question 44 of 60
Quiz ID: q44
What is the primary role of the '=' (equality) symbol in FOL compared to a predicate?
It has a fixed, standard interpretation across all models
It is used to define new predicates
It can have its interpretation specified by an axiom
It is a shorthand for a specific binary predicate like Equals
Question 45 of 60
Quiz ID: q45
Which of these sentences uses a complex term as an argument to a predicate?
Tall(John)
FatherOf(John) = Henry
Loves(John, Mary)
Loves(John, FatherOf(Mary))
Question 46 of 60
Quiz ID: q46
In the context of FOL semantics, what is a 'model'?
A set of syntactic rules for forming sentences
A possible world that specifies truth values for all sentences
A specific interpretation for all constant symbols
A database of facts
Question 47 of 60
Quiz ID: q47
A sentence is 'valid' if it is:
True in some models
True in all models
Contained in the knowledge base
Derivable from the axioms
Question 48 of 60
Quiz ID: q48
A sentence is 'satisfiable' if it is:
True in some model
True in all models
False in all models
Not a well-formed formula
Question 49 of 60
Quiz ID: q49
A sentence is 'unsatisfiable' if it is:
True in some model
True in all models
False in all models
False in some models
Question 50 of 60
Quiz ID: q50
Logical 'entailment', KB ⊨ α, means that:
α is in the knowledge base KB
α is true in every model where KB is true
α is satisfiable
α is a valid sentence
Question 51 of 60
Quiz ID: q51
Which of these is an example of a purely syntactic operation in FOL?
Determining the truth value of a sentence
Checking if a formula is well-formed
Finding a model for a set of sentences
Interpreting a constant symbol
Question 52 of 60
Quiz ID: q52
Which of these is an example of a semantic concept in FOL?
The order of quantifiers in a sentence
The binding of a variable
The truth value of a sentence in a model
The formation of a term from a function
Question 53 of 60
Quiz ID: q53
The property that 'one's grandmother is the mother of one's parent' is best captured by:
A unary predicate
A function symbol
An axiom
A constant symbol
Question 54 of 60
Quiz ID: q54
In FOL, representing 'There are exactly two books on the table' would require:
Existential quantifier and conjunction
Universal quantifier and implication
Existential quantifier, conjunction, inequality, and a uniqueness condition
A single predicate with two arguments
Question 55 of 60
Quiz ID: q55
Which FOL component allows the representation of 'the left leg of John'?
Constant symbol: LeftLegJohn
Predicate symbol: LeftLeg(John)
Function symbol: LeftLeg(John)
Variable: x in LeftLeg(x)
Question 56 of 60
Quiz ID: q56
The statement 'No one is their own parent' is formally expressed as:
∀x ¬Parent(x, x)
∃x ¬Parent(x, x)
¬∀x Parent(x, x)
¬∃x Parent(x, x)
Question 57 of 60
Quiz ID: q57
Which query would find all children of Charles in the knowledge base?
ASK(KB, Child(Charles, x))
ASK(KB, Parent(Charles, x))
ASK(KB, ∃x Child(Charles, x))
ASK(KB, ∀x Parent(Charles, x))
Question 58 of 60
Quiz ID: q58
The axiom ∀x (Person(x) ⇒ (Male(x) ∨ Female(x))) represents:
A definition of Person
A disjunctive property of Persons
An exhaustive categorization of Persons
An equivalence between Person and Gender
Question 59 of 60
Quiz ID: q59
Which logical rule connects the universal quantifier and implication?
Modus Ponens
Universal Instantiation
De Morgan's Law
Existential Generalization
Question 60 of 60
Quiz ID: q60
What is the fundamental difference in how FOL and propositional logic handle the statement 'All humans are mortal'?
FOL uses a single predicate, while propositional logic requires a quantifier
FOL can express it with one quantified sentence, while propositional logic requires a separate sentence for each human
Propositional logic can express it more compactly using implication
There is no difference; both logics handle it the same way
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