LOGIC
Solutions18

# Solutions18 - Chapter 18 Hints and Selected Solutions...

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Chapter 18: Hints and Selected Solutions Section 18.1 (page 498) 18.2 1. This is an allowable change. The language in question does not have any position predicates, so the model for the original world and the modified world are identical. 4. If we make the large cube a dodecahedron, then b 3 would no longer be in the extension of cube , so the model would be different. Hence this is not an allowable change. 7. If we add a dodecahedron to the world, the domain will have to have five objects in it, not just four, so the model would change. Hence this is not an allowable change. 18.3 Hint: The extension Bet of Between would be h b,b 2 ,b 3 i . 18.4 Hint: With two objects in the domain, there are four ordered pairs, and so 2 4 = 16 sets of ordered pairs. Your task it to list them all. 18.5 1. Every 4. Exactly one 18.6 1. Conservativity 4. Monotonedecreasing Section 18.2 (page 507) 18.7 1. g [ y /c ] is the function which assigns b to x and c to y. 4. g [ x /b ] is the same as the original function g . That is, it assigns b to x but that is all. 18.8 1. Appropriate assignments: those that assign values to variables in- cluding both y and z .

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