1. There exist only two types of quantifiers, Universal Quantification and Existential Quantification.

a) True

b) False

View Answer

Explanation: None.

2. Treatment chosen by doctor for a patient for a disease is based on

a) Only current symptoms

b) Current symptoms plus some knowledge from the textbooks

c) Current symptoms plus some knowledge from the textbooks plus experience

d) Only a and b

View Answer

Explanation: None.

3. For resolution to apply, all sentences must be in conjunctive normal form, a conjunction of disjunctions of literals.

a) True

b) False

View Answer

Explanation: None.

4. Translate the following statement into FOL.

“For every a, if a is a philosopher, then a is a scholar”

a) ∀ a philosopher(a) -> scholar(a)

b) ∃ a philosopher(a) -> scholar(a)

c) A is true, B is true

d) A is false, B is false

View Answer

Explanation: None.

5. A _________ is used to demonstrate, on a purely syntactic basis, that one formula is a logical consequence of another formula.

a) Deductive Systems

b) Inductive Systems

c) Reasoning with Knowledge Based Systems

d) Search Based Systems

View Answer

Explanation: Refer the definition of Deductive based systems.

6. Two basic types of inferences are,

1. ____________

2. ____________

a) Reduction to propositional logic, Manipulate rules directly

b) Reduction to propositional logic, Apply modus ponen

c) Apply modus ponen, Manipulate rules directly

d) Convert every rule to Horn Clause, Reduction to propositional logic

View Answer

Explanation: None.

7. The statement comprising the limitations of FOL is/are

a) Expressiveness

b) Formalizing Natural Languages

c) Many-sorted Logic

d) None of the mentioned

View Answer

Explanation:

Expressiveness: The Löwenheim–Skolem theorem shows that if a first-order theory has any infinite model, then it has infinite models of every cardinality. In particular, no first-order theory with an infinite model can be categorical. Thus there is no first-order theory whose only model has the set of natural numbers as its domain, or whose only model has the set of real numbers as its domain. Many extensions of first-order logic, including infinitely logics and higher-order logics, are more expressive in the sense that they do permit categorical axiomatizations of the natural numbers or real numbers. This expressiveness comes at a meta-logical cost, however: by Lindström’s theorem, the compactness theorem and the downward Löwenheim–Skolem theorem cannot hold in any logic stronger than first-order.

Formalizing Natural Languages : First-order logic is able to formalize many simple quantifier constructions in natural language, such as “every person who lives in Perth lives in Australia”. But there are many more complicated features of natural language that cannot be expressed in (single-sorted) first-order logic.

Many-sorted Logic: Ordinary first-order interpretations have a single domain of discourse over which all quantifiers range. Many-sorted first-order logic allows variables to have different sorts, which have different domains

8. A common convention is:

• is evaluated first

• and are evaluated next

• Quantifiers are evaluated next

• is evaluated last.

a) True

b) False

View Answer

Explanation: None.

9. What among the following could the Existential instantiation of,

∃x Crown(x) ^ OnHead(x, Johnny)

a) Crown(John) ^ OnHead(John, Jonny)

b) Crown(y) ^ OnHead(y, Jonny)

c) Crown(x) ^ OnHead(x, Jonny)

d) None of the mentioned

View Answer

Explanation: None.

10. Translate the following statement into FOL.

“For every a, if a is a PhD student, then a has a master degree”

a) ∀ a PhD(a) -> Master(a)

b) ∃ a PhD(a) -> Master(a)

c) A is true, B is true

d) A is false, B is false

View Answer

Explanation: None.

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