22 Slides--Proofs with Quantifiers

22 Slides--Proofs with Quantifiers - 22 Slides-Poofs with...

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22 Slides--Poofs with Quantifiers 2/6/08 1 CS103A 2/6/08 Midterm Exam Tues., Feb. 12 7 - 9 pm Location: TBA Open book (LPL), Open Notes, Crib Sheet Review Session Fri., Feb. 8 3:15 – 4:30 pm Location: Gates B01 Stanford Online, but not broadcast Proofs with Quantifiers Every child is right-handed or intelligent No intelligent child eats liver There is a child who eats liver and onions There is a right-handed child who eats onions 12.23 Proofs with Quantifiers If we know x S(x) , and b is an object, then we can assert S(b) . Tet(b) x Large(x) . . . Large(b) x P(x) . . . P(a) Elim Proofs with Quantifiers If we know x S(x) , and b is an object, then we can assert S(b) . Tet(b) x Large(x) . . . Large(b) Universal Elimination (where a refers to an object) Proofs with Quantifiers If b is an object and we know S(b) , then we can assert x S(x) . Tet(b) . . . x Tet(x) P(a) . . . xP(x) Intro Proofs with Quantifiers If b is an object and we know S(b) , then we can assert x S(x) . Tet(b) . . . x Tet(x) Existential Introduction
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22 Slides--Poofs with Quantifiers 2/6/08 2 x (Tet(x) Green(x)) x (Green(x) Smaller(x, a)) Tet(t) x(Green(x) Smaller(x, a)) 1. 2. 3. 4. 5. 6. 7. 8. 9. x (Tet(x) Green(x)) x (Green(x) Smaller(x, a)) Tet(t) Tet(t) Green(t) Elim Green(t) Smaller(t, a) Elim Green(t) Elim x(Green(x) Smaller(x, a)) 1. 2. 3. 4. 5. 6. 7. 8. 9. 1 2 3, 4 x (Tet(x) Green(x)) x (Green(x) Smaller(x, a)) Tet(t) Tet(t) Green(t) Elim Green(t) Smaller(t, a) Elim Green(t) Elim Smaller(t, a) Elim x(Green(x) Smaller(x, a)) 1. 2. 3. 4. 5. 6. 7. 8. 9. 1 2 3, 4 6, 5 x (Tet(x) Green(x)) x (Green(x) Smaller(x, a)) Tet(t) Tet(t) Green(t) Elim Green(t) Smaller(t, a) Elim Green(t) Elim Smaller(t, a) Elim Green(t) Smaller(t, a) Intro x(Green(x) Smaller(x, a)) Intro 1. 2. 3. 4. 5. 6. 7. 8. 9. 1 2 3, 4 6, 5 6, 7 8 Proofs with Quantifiers If we introduce b as the name of an arbitrary object in the domain of discourse, and we prove S(b) , then we can assert x S(x) .
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22 Slides--Proofs with Quantifiers - 22 Slides-Poofs with...

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