Truth, Equivalence and Consequence

# Truth, Equivalence and Consequence - ⇔ SameSize(b a...

This preview shows page 1. Sign up to view the full content.

Truths, Equivalencies, and Consequences Tautological (Taut Con) First-Order (FO Con) Logical (Ana Con) T R U T H Α ¬ Α ¬ Tet(b) Tet(b) A A Cube(c) Cube(c) (Tautology) a = a (Tet(a) a = b) Tet(b) xCube(x) Cube(e) Cube(e) yCube(y) z (Tet(z) ¬ Tet(z)) (FO Validity) ¬ Smaller(c, c) FrontOf(a, b) BackOf(b, a) (Tet(b) Cube(d)) b d xLarge(x) ¬ xSmall(x) (Logical Truth) E Q U I V A L E N C E ¬ (A B) ¬ A ¬ B ¬ (A B) ¬ A ¬ B P ¬¬ P P Q ¬ P Q P Q (P Q) (Q P) P Q (P Q) ( ¬ Q ¬ P) (Tautological Equivalence) a = b b = a ¬ xCube(x) x ¬ Cube(x) ¬ xCube(x) x ¬ Cube(x) xCube(x) ¬ x ¬ Cube(x) xCube(x) ¬ x ¬ Cube(x) (FO Equivalence) SameSize(a, b)
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ⇔ SameSize(b, a) Larger(a, b) ⇔ Smaller(b, a) FrontOf(b, c) ⇔ BackOf(c, b) LeftOf(d, e) ⇔ RightOf(e, d) (Logical Equivalence) C O N S E Q U E N C E Dodec(a) → Small(a) Dodec(a) Small(a) ¬ (Dodec(a) ∨ Small(a)) ¬ Dodec(a) (Tautological Consequence) Cube(f) f = b Cube(b) ∀ x (Cube(x) → Medium(x)) ∀ x Cube(x) ∀ x Medium(x) ∀ x (Cube(x) → Medium(x)) ∃ x ¬ Medium(x) ∃ x ¬ Cube(x) (FO Consequence) SameShape(b, c) Tet(c) Tet(b) ∀ x (Cube(x) → Large(x)) ∀ x Small(x) ¬ ∃ x Cube(x) ∀ x (x = b → Cube(x)) ∃ x Tet(x) ∃ x (x ≠ b) (Logical Consequence)...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern