Exercise 8.1

A logical knowledge base represents the world using a set of sentences with no explicit structure. An analogical representation, on the other hand, has physical structure that corresponds directly to the structure of the thing represented. Consider a road map of your country as an analogical representation of facts about the country—it represents facts with a map language. The two-dimensional structure of the map corresponds to the two-dimensional surface of the area.

  1. Give five examples of symbols in the map language.

  2. An explicit sentence is a sentence that the creator of the representation actually writes down. An implicit sentence is a sentence that results from explicit sentences because of properties of the analogical representation. Give three examples each of implicit and explicit sentences in the map language.

  3. Give three examples of facts about the physical structure of your country that cannot be represented in the map language.

  4. Give two examples of facts that are much easier to express in the map language than in first-order logic.

  5. Give two other examples of useful analogical representations. What are the advantages and disadvantages of each of these languages?

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