5. Vz[T(x) → 3y[V (») ^ B(z, y)]] Superiority Mandate -33y30[ T(x) ^ T(y) ^ -(z = y) A B(z, v) A B(y, v)] 6. Each to their own 7. -33y(B(z,y) A B(y, z)] Balancing Principle 1 8. Vzvyvz[(B(x,y) A B(y, z)) → -B(z, 2) Balancing Principle 2 9. -J3y3z3w[B(x, v) ^ B(y, z) ^ B(z, w)] Health and Safety 10. -33y3z|¬(y = z) ^ B(z,y) ^ B(z, z)] The 'no straddling' rule - pecullar to Otley [(2 = 6) ++ [(z 'f)g-]zA ]MAZE W Foundational Structural Law An arrangement of vegetables and toys that satisfies all of these axioms will be called a legal arrangment. General guidelines for the following questions • The following questions are a mixture of multiple choice and multiple selection questions. • In the multiple choice questions the possible answers are preceded by circular buttons. You must chose exactly one option from those avalable. • In the multiple selection quetions the possible answers are preceded by square tick boxes. You must chose all correct options. The correct answer could be any selection (including none or all) from the option. What is the minimum number of toys allowed in a legal arrangement? 00 01 O 2 O 3 O 4 O 5
5. Vz[T(x) → 3y[V (») ^ B(z, y)]] Superiority Mandate -33y30[ T(x) ^ T(y) ^ -(z = y) A B(z, v) A B(y, v)] 6. Each to their own 7. -33y(B(z,y) A B(y, z)] Balancing Principle 1 8. Vzvyvz[(B(x,y) A B(y, z)) → -B(z, 2) Balancing Principle 2 9. -J3y3z3w[B(x, v) ^ B(y, z) ^ B(z, w)] Health and Safety 10. -33y3z|¬(y = z) ^ B(z,y) ^ B(z, z)] The 'no straddling' rule - pecullar to Otley [(2 = 6) ++ [(z 'f)g-]zA ]MAZE W Foundational Structural Law An arrangement of vegetables and toys that satisfies all of these axioms will be called a legal arrangment. General guidelines for the following questions • The following questions are a mixture of multiple choice and multiple selection questions. • In the multiple choice questions the possible answers are preceded by circular buttons. You must chose exactly one option from those avalable. • In the multiple selection quetions the possible answers are preceded by square tick boxes. You must chose all correct options. The correct answer could be any selection (including none or all) from the option. What is the minimum number of toys allowed in a legal arrangement? 00 01 O 2 O 3 O 4 O 5
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
5
![Axiomatisation of the Vegetables and Toys Competition
All entries to this competition must strictly obey all formulae in a set of traditional axioms,
otherwise they will be disqualified. The axioms should be interpreted according to the following
specification (key):
Domain of discourse:
All items on the tea tray
V(2)
Item a is a vegetable
T(z)
Item z is a toy
B(x, y)
Item a is balanced on item y.
Notes:
• The possible numbers of entities in the domain is not specified explicitly, but may be
restricted by the axioms that must be satisfied.
• The tea tray itself is not in the domain of discourse. Thus the axioms only apply to the items
on the tray, not the tray. It is required that a single tea tray is used, satisfying British tea tray
regulations and appropriate standards of taste and decency. It should preferably be a family
heirloom.
• The category of vegetable also includes so-called "fruit" -- tomatoes and cucumbers are
welcome, and of course rhubarb. For the real competition, the fruit must have been grown by
the contestent but we ignore this in the present axiomatisation.
• The category of toy includes any toy-like individual item. Prizes are most likely to be awarded
for arrangements involving knitted toys made by the contestant, but this is not a strict
requirement.
Rule Axiom
Rule Name
1. Vz[V(x)V T(x))
Essential Ontological Precondition
2. B3y3z[V(x) ^ V (y) A-(2 = y) A T(z)]
Rule of Plenty
VæVyVzvw[ (V(x) A V(y) A V (2) A V(w))
+ (x = y Vr = z Va = w V
y = z V y = w V z = w) ]
3.
Yorkshire Rule of Parsimony
4. -3æ(V (z) A T(x)]
Requirement of Good Taste](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44dd8c4c-a57a-45ad-b0aa-490ed2f21e7a%2F0649983f-3cf2-41d4-b9f5-2d76f651b5e8%2Fg5zeqkr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Axiomatisation of the Vegetables and Toys Competition
All entries to this competition must strictly obey all formulae in a set of traditional axioms,
otherwise they will be disqualified. The axioms should be interpreted according to the following
specification (key):
Domain of discourse:
All items on the tea tray
V(2)
Item a is a vegetable
T(z)
Item z is a toy
B(x, y)
Item a is balanced on item y.
Notes:
• The possible numbers of entities in the domain is not specified explicitly, but may be
restricted by the axioms that must be satisfied.
• The tea tray itself is not in the domain of discourse. Thus the axioms only apply to the items
on the tray, not the tray. It is required that a single tea tray is used, satisfying British tea tray
regulations and appropriate standards of taste and decency. It should preferably be a family
heirloom.
• The category of vegetable also includes so-called "fruit" -- tomatoes and cucumbers are
welcome, and of course rhubarb. For the real competition, the fruit must have been grown by
the contestent but we ignore this in the present axiomatisation.
• The category of toy includes any toy-like individual item. Prizes are most likely to be awarded
for arrangements involving knitted toys made by the contestant, but this is not a strict
requirement.
Rule Axiom
Rule Name
1. Vz[V(x)V T(x))
Essential Ontological Precondition
2. B3y3z[V(x) ^ V (y) A-(2 = y) A T(z)]
Rule of Plenty
VæVyVzvw[ (V(x) A V(y) A V (2) A V(w))
+ (x = y Vr = z Va = w V
y = z V y = w V z = w) ]
3.
Yorkshire Rule of Parsimony
4. -3æ(V (z) A T(x)]
Requirement of Good Taste
![5. Vz[T(x) + 3y[V (y) ^ B(x, y)]]
Superiority Mandate
-Ba3y3v[ T(x) A T(y) A-(2 = y)
6.
Each to their own
Λ Β(π, υ) Λ (ψ, υ]
7. -3a3y[B(x,y) ^ B(y, x)]
Balancing Principle 1
8. Vævyvz[(B(x, y) ^ B(y, z)) → ¬B(x, z)]
Balancing Principle 2
9. -3Jy3z3w[B(x, y) ^ B(y, z) A B(z,w)]
Health and Safety
10. -3a3yaz(¬(y = z) A B(x, y) A B(x, z)]
The 'no straddling' rule - peculiar to Otley
11. Jarvy[ Vz[¬B(y, z)] + (y = x) ]
Foundational Structural Law
An arrangement of vegetables and toys that satisfies all of these axioms will be called a legal
arrangment.
General guidelines for the following questions
• The following questions are a mixture of multiple choice and multiple selection questions.
• In the multiple choice questions the possible answers are preceded by circular buttons. You
must chose exactly one option from those avalable.
• In the multiple selection quetions the possible answers are preceded by square tick boxes.
You must chose all correct options. The correct answer could be any selection (including
none or all) from the option.
What is the minimum number of toys allowed in a legal arrangement?
01
O 2
O 3
4
O 5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44dd8c4c-a57a-45ad-b0aa-490ed2f21e7a%2F0649983f-3cf2-41d4-b9f5-2d76f651b5e8%2Fvp0q8r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Vz[T(x) + 3y[V (y) ^ B(x, y)]]
Superiority Mandate
-Ba3y3v[ T(x) A T(y) A-(2 = y)
6.
Each to their own
Λ Β(π, υ) Λ (ψ, υ]
7. -3a3y[B(x,y) ^ B(y, x)]
Balancing Principle 1
8. Vævyvz[(B(x, y) ^ B(y, z)) → ¬B(x, z)]
Balancing Principle 2
9. -3Jy3z3w[B(x, y) ^ B(y, z) A B(z,w)]
Health and Safety
10. -3a3yaz(¬(y = z) A B(x, y) A B(x, z)]
The 'no straddling' rule - peculiar to Otley
11. Jarvy[ Vz[¬B(y, z)] + (y = x) ]
Foundational Structural Law
An arrangement of vegetables and toys that satisfies all of these axioms will be called a legal
arrangment.
General guidelines for the following questions
• The following questions are a mixture of multiple choice and multiple selection questions.
• In the multiple choice questions the possible answers are preceded by circular buttons. You
must chose exactly one option from those avalable.
• In the multiple selection quetions the possible answers are preceded by square tick boxes.
You must chose all correct options. The correct answer could be any selection (including
none or all) from the option.
What is the minimum number of toys allowed in a legal arrangement?
01
O 2
O 3
4
O 5
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