A knowledge base contains just one sentence, ∃x AsHighAs (x, Everest).…

Answer: Both sentence (a) and sentence (b) are unsound conclusions.

• Existential instantiation rule: from a sentence of the form ∃x P(x) you may introduce a new constant c and infer P(c). The constant c must be new (it must not already name some specific object in the knowledge base).

• Apply this to the given sentence: from ∃x AsHighAs(x, Everest) we may infer AsHighAs(c, Everest) for a fresh constant c, but we may not replace x directly with an existing name like Everest or Kilimanjaro.

• Why AsHighAs(Everest, Everest) is not justified: concluding this requires assuming Everest is the witness or that the predicate holds for every object. Neither assumption is provided by the existential sentence alone, so the inference is unsound.

• Why AsHighAs(Kilimanjaro, Everest) is not justified: the same reasoning applies — the existential only guarantees some object exists with the property, not that Kilimanjaro (or any particular existing name) is that object.

• When such particular sentences would be sound: only if you had an additional sentence asserting that Everest (or Kilimanjaro) is the witness, or a general axiom guaranteeing the predicate for all objects (for example, a reflexivity axiom).