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Unformatted text preview: CS 245 Winter 2009 Solution Set for Suggested Exercises for Lecture 8 1. You have just joined the ABC FutureHouse company. This company develops software controlled automation systems for houses. You have been given the following specification in English to analyze: If the temperature is at or less than 20 ◦ C, and there are less than 10 people in the room, then turn on the heat. If the temperature is at or less than 20 ◦ C, and there are 10 or more people in the room, then turn on the fan. If the temperature is greater than 20 ◦ C then turn on the air, except if there are 3 or less people in the room, in which case turn on the fan. One and only one of heat, air, and the fan are on at all times. Use a formalization in propositional logic to determine the following: (a) Under what conditions (expressed both in logic and in English) are each of heat, air, or fan required? (b) Is one of heat, air, or fan required for all possible input conditions? If the answer is yes, demonstrate this using natural deduction proof(s). If no, give the case that is not covered, and demonstrate that it is not covered. (c) Is there only one of heat, air, or fan required for all possible input conditions? (i.e., is the specification unambiguous?) If the answer is yes, demonstrate this using semantic tableaux proof(s). If no, give the input conditions for which the specification is ambigu ous, and demonstrate that the specification has this behaviour. If you add any premises in order to carry out the proof for the above parts, demonstrate that your premises are consistent. Soln: (a) Prime Propositions: • T20 – temperature is at or less than 20 ◦ C • 3P – there are less than or equal to 3 people in the room • 3P10 – there are more than 3 and less than 10 people in the room • P10 – there are 10 or more people in the room • Conditions for heat: The temperature is at or less than 20 ◦ C, and there are less than 10 people in the room....
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 Spring '08
 A
 3P, iRiver, ¬3P

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