the symbol ∧ ``lor'' for the symbol ∨ ``lnot'' for the symbol ¬. Given the following three sentences: A) Every mathematician
Note that for this question, you can in addition use
``land'' for the symbol ∧
``lor'' for the symbol ∨
``lnot'' 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 I such that I 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, lnot 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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