1. There exist only two types of quantifiers, Universal Quantification and Existential Quantification.
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
3. A knowledge-based agent can combine general knowledge with current percepts to infer hidden aspects of the current state prior to selecting actions.
Explanation: Refer definition of Knowledge based agents.
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
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
Explanation: Refer the definition of Deductive based systems.
6. ‘α |= β ‘(to mean that the sentence α entails the sentence β) if and only if, in every model in which α is _____, β is also _____.
a) True, true
b) True, false
c) False, true
d) False, false
Explanation: Refer the definition of law of entailment.
7. The statement comprising the limitations of FOL is/are
b) Formalizing Natural Languages
c) Many-sorted Logic
d) None of the mentioned
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.
9. How many proposition symbols are there in artificial intelligence?
Explanation: The two proposition symbols are true and false.
10. How many logical connectives are there in artificial intelligence?
Explanation: The five logical symbols are negation, conjunction, disjunction, implication and bi-conditional.
Sanfoundry Global Education & Learning Series – Artificial Intelligence.