helor is not married t orge is a mathematicia
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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.
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![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 /, 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 / 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4d1c387-98a9-472d-8b3d-84eb079524b7%2F8de8ee37-68c7-4cf4-8c14-0ee90276104c%2Ffet6xzb_processed.png&w=3840&q=75)
Transcribed Image Text: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 /, 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 / 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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