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Summary: Brachman and Levesque, Chapter 3 exercise 1. An exam question may
look like this (although obviously not exactly this question) and will be worth
25 points.
Question Consider the following piece of knowledge:
Tony, Mike and John belong to the Alpine Club. Every member of the
Alpine Club who is not a skier is a mountain climber. Mountain climbers do
not like rain, and anyone who does not like snow is not a skier. Mike dislikes
whatever Tony likes, and likes whatever Tony dislikes. Tony likes rain and snow.
(a) Prove that the given sentences logically entail that there is a member of
Alpine Club who is a mountain climber but not a skier.
(b) Suppose we had been told that Mike likes whatever Tony dislikes, but we
had not been told that Mike dislikes whatever Tony likes. Prove that the
resulting set of sentences no longer logically entails that there is a member
of Alpine Club who is a mountain climber but not a skier.
Answer The answer given during one of the lectures used the following pred-
icates and constants:
Member unary predicate meaning a member of the Alpine Club
Skier unary predicate meaning a skier
Climber unary predicate meaning a climber
Likes binary predicate where Likes(x, y) means that x likes y
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