Note that for this question, you can in addition use ``land" for the symbol A ` `lor" for the symbol V ``Inot" for the symbol- Given the following three sentences: A) Every mathematician is married to an engineer. B) A bachelor is not married to anyone. C) If George is a mathematician, then he is not a bachelor. a) Convert A,B,C into three FOL sentences, where Mn(x): x is a mathematician. Er(x): x is an engineer. Md(x,y): x is married to y. Br(x): x is a bachelor. george: George is a constant. b) Show that A does-not-entail C. (Hint: Consider defining an interpretation / such that / models A, but does-not-model C.) c) Show that (A,B) entails C. (Hint: For a given interpretation I, consider two difference cases, the case where Mn(george) is true, and the case Mn(george) is false. For both cases, argue that it is always that I models C). d) Convert A,B, Inot C into a set of clausal forms, number your clauses. (Note that C is negated here!) e) Derive the empty clause from the set of clauses obtained in d), using resolutions. Your answer should be in clearly steps, one example step is like: Step 5: C3 resolves with C7 on literal L, with substitution x/george, resulting C8: [Er(x)].

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
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Note that for this question, you can in addition use
``land” for the symbol
``lor" for the symbol V
` `Inot" for the symbol ¬
Given the following three sentences:
A) Every mathematician is married to an engineer.
B) A bachelor is not married to anyone.
C) If George is a mathematician, then he is not a bachelor.
a) Convert A,B,C into three FOL sentences, where
Mn(x): x is a mathematician.
Er(x): x is an engineer.
Md(x,y): x is married to y.
Br(x): x is a bachelor.
george: George is a constant.
b) Show that A does-not-entail C. (Hint: Consider defining an interpretation / such
that / models A, but does-not-model C.)
c) Show that {A,B} entails C. (Hint: For a given interpretation I, consider two
difference cases, the case where Mn(george) is true, and the case Mn(george) is false.
For both cases, argue that it is always that I models C).
d) Convert A,B, Inot C into a set of clausal forms, number your clauses. (Note that C
is negated here!)
e) Derive the empty clause from the set of clauses obtained in d), using resolutions.
Your answer should be in clearly steps, one example step is like:
Step 5: C3 resolves with C7 on literal L, with substitution x/george, resulting C8:
[Er(x)].
f) Is there an SLD derivation of the empty clause? Explain why or why not.
Transcribed Image Text:Note that for this question, you can in addition use ``land” for the symbol ``lor" for the symbol V ` `Inot" for the symbol ¬ Given the following three sentences: A) Every mathematician is married to an engineer. B) A bachelor is not married to anyone. C) If George is a mathematician, then he is not a bachelor. a) Convert A,B,C into three FOL sentences, where Mn(x): x is a mathematician. Er(x): x is an engineer. Md(x,y): x is married to y. Br(x): x is a bachelor. george: George is a constant. b) Show that A does-not-entail C. (Hint: Consider defining an interpretation / such that / models A, but does-not-model C.) c) Show that {A,B} entails C. (Hint: For a given interpretation I, consider two difference cases, the case where Mn(george) is true, and the case Mn(george) is false. For both cases, argue that it is always that I models C). d) Convert A,B, Inot C into a set of clausal forms, number your clauses. (Note that C is negated here!) e) Derive the empty clause from the set of clauses obtained in d), using resolutions. Your answer should be in clearly steps, one example step is like: Step 5: C3 resolves with C7 on literal L, with substitution x/george, resulting C8: [Er(x)]. f) Is there an SLD derivation of the empty clause? Explain why or why not.
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