A knowledge base contains only \(\exists x\,AsHighAs(x,Everest)\). Apply existential instantiation by introducing a fresh witness constant. Treat Kilimanjaro solely as a new symbol with no previously assigned geographical referent. (a) \(AsHighAs(Everest,Everest)\) (b) \(AsHighAs(Kilimanjaro,Everest)\) Which applications are permitted by the fresh-constant rule?
(a) is not permitted but (b) is permitted.
Existential instantiation introduces a fresh constant as a name for an unspecified witness. Everest already occurs in the knowledge base, so (a) violates that rule; Kilimanjaro is fresh under the stated convention, so (b) is permitted. This preserves satisfiability by extending an interpretation with a witness name; it does not establish a geographical fact about the actual Kilimanjaro.
Important Questions from First Order Logic - Teaching
Consider the statements below:
“There is a country that borders both India and Nepal.”
Which of the following represents the above sentence correctly?If f(x) = x is my friend, and p(x) = x is perfect. then correct logical translation of the statement “some of my friends are not perfect” is _______.
Equivalent logical expression for the Well Formed Formula (WFF),
\(\sim(\forall x)\,F[x]\)
is
Let P(m, n) be the statement “m divides n” where the Universe of discourse for both the variables is the set of positive integers. Determine the truth values of the following propositions.
(a) \(\exists m \forall n P(m, n)\) (b) \(\forall n P(1, n)\) (c) \(\forall m \forall n P(m, n)\)
Codes :
________predicate calculus allows quantified variables to refer to objects in the domain of discourse and not to predicates or functions.
