This set of Artificial Intelligence Multiple Choice Questions & Answers (MCQs) focuses on “First-Order Logic”.
1. There exist only two types of quantifiers, Universal Quantification and Existential Quantification.
2. 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) All of the mentioned
d) None of the mentioned
3. 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.
4. The statement comprising the limitations of FOL is/are ____________
b) Formalizing Natural Languages
c) Many-sorted Logic
d) All of the mentioned
Explanation: 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.
5. A common convention is:
• is evaluated first
• and are evaluated next
• Quantifiers are evaluated next
• is evaluated last.
6. A Term is either an individual constant (a 0-ary function), or a variable, or an n-ary function applied to n terms: F(t1 t2 ..tn).
Explanation: Definition of term in FOL.
7. First Order Logic is also known as ___________
a) First Order Predicate Calculus
b) Quantification Theory
c) Lower Order Calculus
d) All of the mentioned
8. The adjective “first-order” distinguishes first-order logic from ___________ in which there are predicates having predicates or functions as arguments, or in which one or both of predicate quantifiers or function quantifiers are permitted.
a) Representational Verification
b) Representational Adequacy
c) Higher Order Logic
d) Inferential Efficiency
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