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Unformatted text preview: x Large(x) and another 1. " x (Dodec(x) Large(x)) 2. " x (Large(x) FrontOf(x, f) 3. 4. 5. 6. 7. 8 . " x (Dodec(x) FrontOf(x, f) Exercises: 13.2 and 13.3 Existential quantifier rules: Existential introduction ( $ Intro): S(c) : $ x S(x) Existential introduction allows us to write a general existential claim for any statement that is true of some constant (named object) in our domain of discourse. $ Intro in use: 1. Dodec(a) 2. Cube(b) Dodec(b) 3. Small(c) Large(d) 4. Tet(e) Medium(f) 5. $ x Dodec(x) $ Intro: 1 6. $ y (Cube(y) Dodec(y)) $ Intro: 2 7. $ z (Small(z) Large(d)) $ Intro: 3 8. $ x $ y (Tet(x) Medium(y)) $ Intro: 4 Existential elimination ( $ Elim): $ x S(x) c S(c) : Restriction: c must not occur outside the subproof : where it is introduced. Q Q $ Elim in use: 1. " x (Cube(x) Large(x)) 2. " x (Large(x) LeftOf(x, b) 3. $ x Cube(x) 4. 5. 6. 7. 8. 9. 10. 11. $ x (Large(x) LeftOf(x, b)) Exercises: 13.13 (same as 12.4) and 12.7...
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 Fall '06
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