# Assignment 3

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

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

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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?

symbol of arity 2 and succ is a function symbol of arity 1?

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Is ∀z S(x,y) a well-formed formula?

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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)?

### Accepted Answers:

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)?

### Accepted Answers:

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?

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?

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

A ⊃ B

C

----------

∴ D

A ⊃ B

C

----------

∴ D

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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?

in taste” where mango belongs to the fruits domain?

### Accepted Answers:

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” ?

which is sweet in taste” ?

### Accepted Answers:

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

### Accepted Answers:

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

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