A knowledge base contains just one sentence, ∃x AsHighAs (x, Ever
A knowledge base contains just one sentence, ∃x AsHighAs (x, Everest). Consider the
following two sentences obtained after applying existential instantiation.
(a) AsHighAs (Everest, Everest)
(b) AsHighAs (Kilimanjaro, Everest)
Which of the following is correct with respect to the above sentences?
A. Both sentence (a) and sentence (b) are sound conclusions.
B. Both sentence (a) and sentence (b) are unsound conclusions.
C. Sentence (a) is sound but sentence (b) is unsound.
D. Sentence (a) is unsound but sentence (b) is sound.
Please scroll down to see the correct answer and solution guide.
Right Answer is: D
SOLUTION
Concept:
Predicate logic deals with predicates which are propositions, consists of variables. Two quantifies in predicate logic are there exist (∃) and for all (∀).
Explanation:
Given statement is:
∃x AsHighAs (x, Everest).
It is comparing one element with other element. It means, there exists a element x which is as high as Everest. So, for comparison we have x and Everest should be different.
(a) AsHighAs (Everest, Everest)
After applying existential quantifies, this statement becomes.
∃Everest AsHighAs (Everest, Everest) : it means there exist an Everest which is as high as Everest. There is no meaning of this sentence. As we are comparing same elements. It does not sounds good.
(b) AsHighAs (Kilimanjaro, Everest)
After applying existential quantifies, this statement becomes.