________predicate calculus allows quantified variables to refer to objects in the domain of discourse and not to predicates or functions.
First-order
In first-order predicate calculus, the quantifiers \(\forall\) and \(\exists\) range only over individual objects of the domain.
Second-order and higher-order logics also allow quantification over predicates and functions, while zero-order (propositional) logic has no quantified variables at all.
So restricting quantified variables to objects defines first-order logic.
Hence, First-order.
Similar Questions
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 :
The notation \(\exists! x P(x)\) denotes the proposition “there exists a unique \(x\) such that P(\(x\)) is true”.
Give the truth values of the following statements :
I. \(\exists! x P(x) \rightarrow \exists x P(x)\)
II. \(\exists! x \neg P(x) \rightarrow \neg \forall x P(x)\)
The kind of symbols for basic syntactic elements of first-order logic are
A. Constant
B. Domain
C. Predicate
D. Temporal
E. Function
Choose the correct answer from the options given below:
Translate ∀x∃y(x<y) in English. Consider domain as a real number for both the variables.
Let L (x, y) be the statement “x loves y” where the domain for both x and y consists of all people in the world. Use quantifiers to express “Joy is loved by everyone”.
What is the process of capturing inference process as a single inference rule?
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?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?
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 :
