19 Slides--Logic of Quantifiers

19 Slides--Logic of Quantifiers - CS103A Handout #19...

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CS103A Handout #19 Slides--Logic of Quantifiers 2/1/08 1 CS103A 2/1/08 Midterm Exam Tues., Feb. 12 7 - 9 pm Location: TBA x Cube(x) x Cube(x) ¬ x Cube(x) ¬ x Cube(x) x ¬Cube(x) x ¬Cube(x) Describe a world for each of these x (Professor(x) Smart(x)) x Professor(x) x Smart(x) x (Professor(x) Smart(x)) x Professor(x) x Smart(x) Tautologies with Quantifiers P ¬P ( x Cube(x)) ( x ¬Cube(x)) ( x Cube(x)) x Cube(x)) Truth-Functional Form -- Replace quantified constituents with a letter -- Replace remaining atomic constituents with a letter -- Reuse the same letter for identical constituents -- Maintain connectives outside of quantifiers -- Check the result [ z (Cube(z) Large(z)) Cube(b) ] Large(b) [ ( x Cube(x) → ∀ x Small(x)) ¬ x Small(x) ] ¬ x Cube(x) A way to determine whether a quantified sentence is a tautology. Cube(a)
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19 Slides--Logic of Quantifiers - CS103A Handout #19...

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