Resolution An Example

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ResolutionAn Example
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Ancient Rome

• Marcus was a male Roman who tried to kill Caesar.
  He was also a Pompeian. All Pompeians were
  Romans. Caesar was a ruler. All Romans were
  either loyal to Caesar or hated him. Everyone
  has someone to whom he or she is loyal. Men only
  try to kill rulers they are not loyal to. Marcus
  tried to kill Caesar.

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Ancient Rome in FOPL

• man(marcus)
• roman(marcus)
• pompeian(marcus)

trykill(marcus,caesar) ruler(caesar)
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Ancient Rome in CNF

• man(marucs)
• Pompeian(marcus)
• Roman(marcus)
• ruler(caesar)
• pompeian(X-1) V roman(X-1)
• roman(X-2) V
• loyal_to(X-2,caesar)
• V hate(X-2,caesar)
• loyal_to(z,f(z))
• man(X-3) V ruler(X-4) V
• trykill(X-3,X-4) V loyal_to(X_3,X-4)
• trykill(marcus,caesar)

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Does Marcus Hate Caesar?

• Using the resolution inference rule
• (p V Q) (Q V R) gt P V R
• Work out the example

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Observations

• Resolution takes a set of clauses that are all
  true based on outside information
• Generates new clauses that logically follow from
  the original
• A contradiction occurs when a clause which
  logically follows cant be satisfied
• Whenever possible resolve with a clause with a
  single predicate
• Get the negated statement into the mix ASAP
• If a contradiction exists resolution will find
  it.
• If a contradiction does not exist, one indication
  is that no progress is being made. Quit after a
  predetermined effort.