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Hello I can't find the answer thanks for the help Exercise F (= problem 3, exercises 7th week) 1. A predicate logic formula is called
Hello I can't find the answer thanks for the help
Exercise F (= problem 3, exercises 7th week) 1. A predicate logic formula is called satisfiable, if there exists an interpretation that makes it true. Explain how the tableau method can be used to determine if a predicate logic formula is satisfiable. Hint: What must the root formula of the tableau be? Then what does it mean if the tableau with this root formula closes? 2. Consider the following story about a barber: Assume that there is a town with just a single male barber, and that each man in town himself makes sure to be shaved: some by shaving themselves, some by going to the barber's. It now seems reasonable to think that the barber satisfies the following rule: he shaves exactly those men that do not shave themselves. Briefly explain the problem of having a male barber defined by shaving exactly those men that do not shave themselves. 3. Let the be given a constant symbol b and a binary predicate symbol B. Besides, let there be given an interpretation F by: . = dom(F) = all men in town. bu = the barber. BF is the predicate _ shaves _. . Write a formula that in the given interpretation expresses the following: "The barber shaves exactly those that do not shave themselves." 4. Show that the formula from the question is not satisfiable. That is, that there can be no male barber that shaves exactly those that do not shave themselves. Use the tableau method to show it (cf. the first question of the assignment). Exercise F (= problem 3, exercises 7th week) 1. A predicate logic formula is called satisfiable, if there exists an interpretation that makes it true. Explain how the tableau method can be used to determine if a predicate logic formula is satisfiable. Hint: What must the root formula of the tableau be? Then what does it mean if the tableau with this root formula closes? 2. Consider the following story about a barber: Assume that there is a town with just a single male barber, and that each man in town himself makes sure to be shaved: some by shaving themselves, some by going to the barber's. It now seems reasonable to think that the barber satisfies the following rule: he shaves exactly those men that do not shave themselves. Briefly explain the problem of having a male barber defined by shaving exactly those men that do not shave themselves. 3. Let the be given a constant symbol b and a binary predicate symbol B. Besides, let there be given an interpretation F by: . = dom(F) = all men in town. bu = the barber. BF is the predicate _ shaves _. . Write a formula that in the given interpretation expresses the following: "The barber shaves exactly those that do not shave themselves." 4. Show that the formula from the question is not satisfiable. That is, that there can be no male barber that shaves exactly those that do not shave themselves. Use the tableau method to show it (cf. the first question of the assignment)Step by Step Solution
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