From: Artificial Intelligence - A Modern Approach, by Stuart Russell and Peter N

Question

From: Artificial Intelligence - A Modern Approach, by Stuart Russell and Peter Norvig.

8.8 Does the fact ¬Spouse(George, Laura) follow from the facts Jim ? George, and Spouse(Jim, Laura)? If so, give a proof; if not, supply additional axioms as needed. What happens if we use Spouse as a unary function symbol instead of a binary predicate?

Explanation / Answer

There is an extra axiom needed: (Male(x) and Spouse(x, y)) => Female(y) Answer for exercise 8.8 in the 3nd edition: No, not(Spouse(George, Laura)) does not follow from the given facts. We need the additional axiom: (Spouse(x, y) and (z != x)) => not(Spouse(z, y)) If Spouse becomes a unary function, then no additional axiom is needed. Then, the facts would be written as: Jim != George Spouse(Laura) = Jim and the statement not(Spouse(Laura) = George) can be proven as follows: ((Spouse(Laura) = Jim) and (Jim != George)) => not(Spouse(Laura) = George) If Spouse is a function, then it can only return a single value for each argument (such as Laura). hope it helps.god bless you.

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