NPTEL » Fundamentals Of Artificial Intelligence Week 5 answers

 

1 point

1) In First Order Logic, the elements of a conceptualization include______

Well-formed expression

2) A sentence in a formal language is true if and only if it accurately describes the world according to our conceptualization. ___________ is a mapping between elements of the language and elements of a conceptualization

 A. Declarative semantics

 

3)Facts and rules that attempt to capture all of the (important) facts and concepts about a domain are referred to as __________

 A. Definitions

4)P, Q and R are logical propositions. Identify the statements as tautology, and / or contradiction?

(i). ((P∨Q)∧R)↔((P∧R)∨(Q∧R))$((P\vee Q)\wedge R)\leftrightarrow ((P\wedge R)\vee (Q\wedge R))$
(ii). (P↔Q)∧(Q↔R)∧¬(P↔R)$(P\leftrightarrow Q)\wedge (Q\leftrightarrow R)\wedge \neg (P\leftrightarrow R)$

  B. I. Contradiction; II. Tautology

5) In existential instantiation, the variable is replaced by a brand-new constant not occurring in this or any other sentence in the KB. The constant so introduced is called a ________ constant

 A. Skolem 

6) Consider the predicate Likes(x,y): x likes y. 

Everyone likes ice cream. Is it possible to convey the same meaning using an existential statement? If yes, give the existential statement. 

  B. Yes>∀x Likes(x,Icecream)

7) ___________ helps immensely in search as it dramatically reduces the number of resolvents that can be inferred from two input clauses 

 A. Conjunctive Normal Form

8) For the following pair of atomic sentences, give the most general unifier, if it exists:

 (i). Older(Father(y), y)
  
  (ii). Older(Father(x), John)

   ans :C. {y/John, x/John}

9) Write the FOL formula obtained by introducing the skolem function Support(x) in the NEXT step towards arriving at the Clausal Normal Form for the following 

∀x[¬Brick(x)∨(∃y[On(x,y)∧¬Pyramid(y)]∧∀y[¬On(x,y)∨¬On(y,x)])]$\forall x[\neg Brick(x)\vee (\exists y[On(x,y)\wedge \neg Pyramid(y)]\wedge \forall y[\neg On(x,y)\vee \neg On(y,x)])]$

 A.∀x[¬Brick(x)∨([On(x,Support(x))∧¬Pyramid(y)]∧∀y[¬On(x,y)∨¬On(y,x)])]

10 )A definition of a predicate is a biconditional, and can be decomposed into a necessary and sufficient descriptions. Which of the following statement are true with regards to definition of `Brother’

I. Being a `Male’ is a necessary condition for being a `Brother’, but it is not sufficient

II. Being a `Male’ `Sibling’ is a necessary and sufficient condition for being a `Brother’

 A. I Only

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