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:
A, C, E only
In Russell and Norvig's presentation of first-order logic, the basic syntactic elements are the symbols that stand for objects, relations and functions. There are exactly three kinds of such symbols.
A. Constant symbols stand for objects (for example Richard, John) — a basic element.
C. Predicate symbols stand for relations (for example Brother, OnHead) — a basic element.
E. Function symbols stand for functions (for example LeftLeg) — a basic element.
B. Domain is not a symbol; it is the set of objects of a model, part of the semantics rather than the syntax.
D. Temporal is not a symbol kind of first-order logic at all; time is handled by temporal logics, which extend first-order logic.
So the elements are A, C and E. Any combination containing Domain or Temporal is wrong, which rules out the other three choices.
A, C, E only option is correct.
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.
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. \(\exists! x \neg P(x) \rightarrow \neg \forall x P(x)\)
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?
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 :