What is the process of capturing inference process as a single inference rule?
Generalized modus ponens
In first-order logic, reaching a conclusion from quantified rules normally needs several steps: Universal Instantiation to replace variables, And-Introduction to combine facts, and then Modus Ponens. The lifted rule that packs all of these into one step is Generalized Modus Ponens.
For atomic sentences pi, pi' and q, if a substitution θ makes SUBST(θ, pi') = SUBST(θ, pi) for every i, then from p1', …, pn' and (p1 ∧ … ∧ pn ⇒ q) we infer SUBST(θ, q) in a single step. For example, from King(John), Greedy(John) and ∀x King(x) ∧ Greedy(x) ⇒ Evil(x), it infers Evil(John) directly with θ = {x/John}.
“Ponens” alone is not a rule; clauses are the form in which sentences are written for resolution; variables are the symbols being substituted. None of them is an inference rule that captures the whole process.
Generalized modus ponens option is correct.
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 :
________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. \(\exists! x \neg P(x) \rightarrow \neg \forall x P(x)\)
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”.
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 :
