Quiz Tuesday Nov. 24 Logic
1. Propositional Logic
[1a.] Is resolution a sound and complete inference algorithm for propositional logic?
[1b.] Is the knowledge base: KB  {A  (B  C  D  A)} in CNF form?
[1c.] Is the KB from 1b in Horn form?
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[1d.] Prove, using resolution that (B  C  D) is entailed by the KB.
2. Mathematical Theorems in FOL
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[2a.] Express the following theorem in FOL. Use property “Integer(x)” (true when x
is integer) and relations “LargerThan(x,m)” (true when x>m) and
“PowerSum(a,b,c,n)” (true when an + bn = cn for any four integers a,b,c,n). Use
existential quantification.
“Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy
the equation an + bn = cn for any integer value of n greater than two.”
[2b.] Using de Morgan’s law, rewrite the above sentence into an equivalent sentence
which only uses universal quantification.
[2c.] Goldbach's conjecture is one of the oldest unsolved problems in number theory
and in all of mathematics. It states:
“Every even integer greater than 2 is a number that can be expressed as the sum of
two primes.”
Express Goldbach’s conjecture in FOL. In addition the properties and relations in a)
you can also use: “Even(m)” (true when m is even), “Prime(p)” (true when p is
prime). Hint: you will need all relations and properties defined under a).