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# Assignment 3

What does the logical part of the alphabet of FOL describe?

What does the non-logical part of the alphabet of FOL describe?

Given a domain D of natural numbers {0, 1, 2, 3, ... } which of the following is/are valid term(s) in FOL, where x and y are variables, product is a function
symbol of arity 2 and succ is a function symbol of arity 1?

Is ∀z S(x,y) a well-formed formula?

Given L(R,F,C) where R={P,Q,S}, F={f,g,h}, C={a,b,c} and the set of variables is {x,y,z}, which of the following are formulas of L(R,F,C)?

Given L(R,F,C) where R={P,Q,S}, F={f,g,h}, C={a,b,c} and the set of variables is {x,y,z}, which of the following are sentences of L(R,F,C)?

Consider the following statements:

S1: ∀x (Politician(x) ⊃ Honest(x))
S2: ∃x (Politician(x) ∧ Honest(x))

Which of the following is/are true for a knowledge base (KB) with a set of people as its domain?

For the Modified Modus Ponens rule below when can one add D to the KB?

A ⊃ B
C
----------
∴ D

Given the domain of names of all fruits and the statement “All elements are sweet in taste”, which rule of inference can be applied to infer “mango is sweet
in taste” where mango belongs to the fruits domain?

From the statement “mango is sweet in taste” where mango belongs to the fruits domain, which rule of inference can be applied to infer “there is something
which is sweet in taste” ?

Consider two clauses P(x, f(x)) and P(f(y), y). What is the result of unification?

Given the sentences and their respective domains below, which of the following sentence(s) is/are true?