AI : First Order Logic (Questions And Answers)

Assignment 3

What does the logical part of the alphabet of FOL describe?

A set of constant symbols

The set of variables, e.g. {x1, x2, …, x, y, ...}

The set of logical connectives

The set of quantifiers, e.g. {∀, ∃}

The equality symbol  

Accepted Answers:

The set of variables, e.g. {x1, x2, …, x, y, ...}

The set of logical connectives

The set of quantifiers, e.g. {∀, ∃}

The equality symbol 

What does the non-logical part of the alphabet of FOL describe?

The set of function symbols

The set of variables, e.g. {x1, x2, .., xn}

The set of relational symbols

The set of quantifiers, e.g. {∀, ∃}

The set of constant symbols 

Accepted Answers:

The set of function symbols

The set of relational symbols

The set of constant symbols 

Given a domain D of natural numbers {0, 1, 2, 3, ... } which of the following is/are valid term(s) in FOL, where x and y are variables, product is a function
    symbol of arity 2 and succ is a function symbol of arity 1?

product(5, x)

succ(product(4, 5))

product(succ(x), 16)

succ(product(7))

product(product(5, 7), y)

product(product(5, 7), product(6, 7))

product(4, 7, 11)

product(succ, 13) 

Accepted Answers:

product(5, x)

succ(product(4, 5))

product(succ(x), 16)

product(product(5, 7), y)

product(product(5, 7), product(6, 7))

Is ∀z S(x,y) a well-formed formula?

Yes

No

It depends on the interpretation function.

Accepted Answers:

Yes 

Given L(R,F,C) where R={P,Q,S}, F={f,g,h}, C={a,b,c} and the set of variables is {x,y,z}, which of the following are formulas of L(R,F,C)?

 

Accepted Answers:

Given L(R,F,C) where R={P,Q,S}, F={f,g,h}, C={a,b,c} and the set of variables is {x,y,z}, which of the following are sentences of L(R,F,C)?

 

Accepted Answers:

Consider the following statements:

 S1: ∀x (Politician(x) ⊃ Honest(x))
 S2: ∃x (Politician(x) ∧ Honest(x))

 Which of the following is/are true for a knowledge base (KB) with a set of people as its domain?

If S1 is satisfied by the KB, then everyone is honest.

It S2 is satisfied by the KB, then there is at least one person who is a politician and who is honest.

If S1 is satisfied by the KB, then it implies that if a person is a politician then she is honest.

If S1 is satisfied by the KB, then S2 is also satisfied by the KB.  

Accepted Answers:

It S2 is satisfied by the KB, then there is at least one person who is a politician and who is honest.

If S1 is satisfied by the KB, then it implies that if a person is a politician then she is honest.

For the Modified Modus Ponens rule below when can one add D to the KB?

A ⊃ B
C
----------
∴ D

When there is a substitution θ s.t. Bθ = C and D = Aθ

When there is a substitution θ s.t. Aθ = C and B = Dθ

When there is a substitution θ s.t. Aθ = C and D = Bθ

When there is a substitution θ s.t. Cθ = B and D = Cθ

Accepted Answers:

When there is a substitution θ s.t. Aθ = C and D = Bθ

Given the domain of names of all fruits and the statement “All elements are sweet in taste”, which rule of inference can be applied to infer “mango is sweet
 in taste” where mango belongs to the fruits domain?

Modus ponens

Common sense

Generalization

Universal Instantiation

Accepted Answers:

Universal Instantiation

From the statement “mango is sweet in taste” where mango belongs to the fruits domain, which rule of inference can be applied to infer “there is something
which is sweet in taste” ?

Modus tollens

Common sense

Generalization

Universal Instantiation  

Accepted Answers:

Generalization

Consider two clauses P(x, f(x)) and P(f(y), y). What is the result of unification?

Cannot be unified

{x/f(y), y/f(x)}

{x/y}

{x/f(f(x)), y/f(x)}  

Accepted Answers:

Cannot be unified

Given the sentences and their respective domains below, which of the following sentence(s) is/are true?

∀x ( (x>2) ⊃ (x > 3) ), x Є Real Numbers

∀x ( (x>2) ⊃ (x >3) ), x Є Integers

∀x ∃y ( x + y = 10), x, y Є Positive Integers

∀x ∃y ( x + y = 10), x, y Є Integers

∃x ∃y ( x + y = 10), x,y Є Positive Integers

∀x ∀y ∃z ((x + y) + z) = 10), x,y,z Є Natural Numbers  

Accepted Answers:

∀x ∃y ( x + y = 10), x, y Є Integers

∃x ∃y ( x + y = 10), x,y Є Positive Integers