CS:4420代做、代写Intelligence留学生、Python，Java/c++编程设计代做

日期：2019-03-28 09:02

CS:4420 Artificial Intelligence

Spring 2019

Homework 4

Part A

Due: Friday, March 29 by 11:59pm

This assignment has two parts, A and B, both to be done individually. This document describes

Part A which is a written assignment.

Write your solutions in a text editor or word processor and submit on ICON a printout of the file

in PDF format. Make sure you add your name. Handwritten solutions are acceptable only if your

handwriting is legible and you submit a scan of the work and as a single file. No photographs,

please.

1 Domain Modeling in First-Order Logic

1. Do Problem 8.9 from the textbook. Report just the question number and for each alternative

in the question your classification.

Example:

f. (i) - (2)

(ii) - (1)

(iii) - (3)

(iv) - (1)

2. For this problem and the next you should use only the relation and function symbols in

Figure 1. Do not introduce your own symbols.

(a) Translate each of the following FOL sentences in good, natural English (they should have

no x’s or y’s). Note that, for readability, square brackets are also used as parentheses.

i. x [P erson(x)y (P erson(y) ∧ Needs(x, y))]

ii. x [Loves(M ary, x)  Loves(John, x)]

iii. x [P erson(x) y (Has(x, y) ∧ Heart(y))]

iv. x [P erson(x)y z (P arent(x, y) ∧ P arent(x, z) ∧ (y = z))]

v. s [(Student(s) ∧ Likes(s, AI)) Likes(s, CS4420)]

vi. [x y (P erson(y)  Likes(y, x))]

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Predicate Intended Meaning

American(x) x is American

Bug(x) x is a (software) bug

Class(x) x is a class

Drinks(x,y) x drinks y

From(x,y) x is from y

Good(x) x is good

Grandparent(x,y) y is a grandparent of x

Has(x,y) x has y

Heart(x) x is a heart

In(x,y) x is in y

Knows(x,y) x knows y

Likes(x,y) x likes y

Loves(x,y) x loves y

Museum(x) x is a museum

Predicate Intended Meaning

Needs(x,y) x needs y

Parent(x,y) y is a biological parent of x

Person(x) x is a person

Program(x) x is a program

Student(x) x is a student

Teaches(x,y) x teaches y

Tease(x,y,z) x teases y at time z

Time(x) x is a time

Visited(x,y) x visited y

Wants(x,y) x wants y

Wine(x) x is a kind of wine

Wrote(x,y) x wrote y

Function Intended Meaning

mother(x) the biological mother of x

Figure 1:

vii. x y [Bug(x) ∧ P rogram(y) ∧ W rote(John, y) ∧ In(x, y)]

viii.y Needs(M ary, y)

ix.x P arent(x, mother(x))

x.x (P erson(x) Knows(x, mother(x)))

(b) Translate each of the following English statements to FOL. Use only logical symbols

from the set {, , ∧, ∨, , , , =}. You can use the constant symbols F red, Jane,

F rance, Louvre, with the expected meaning.

Make sure you use parentheses to avoid ambiguous readings of your sentences.

i. Students love museums.

ii. Not every student likes a good museum.

iii. Some Americans like wines from France.

iv. Americans who love wines from France dislike American wines.

v. Jane visited all the museums in France except the Louvre.

vi. Fred knows any museum visited by Jane.

vii. Everyone knows someone from France.

viii. Fred likes all kinds of wine.

ix. Fred drinks only wine.

x. Everybody has exactly two parents.

xi. Not everyone knows someone with a French mother.

xii. Those who know Jane’s mother love her.

xiii. You cannot dislike people you love.

xiv. Jane only loves people with a good heart.

xv. No one has something that everybody wants.

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2 Validity and Entailment in FOL with equality

For the problems below it is helpful to recall that all interpretations in FOL are assumed to have

a non-empty domain.

1. For each FOL sentence below say whether it is valid or not and briefly explain why. Specifi-

cally, for each valid sentence argue informally but precisely why every possible interpretation

makes the sentence true; for each invalid sentence describe an interpretation that makes the

sentence false.

2. Optional, Extra credit

Let Γ be the knowledge base {M arried(J im, Laura), (J im = George)} and

let α be the sentence ?M arried(George, Laura).

(a) Argue informally but convincingly that Γ does not entail α.

(b) Provide enough FOL sentences that when added to Γ ensure that Γ |= α.

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