Logic1019 - Tableaux for first-order ]= logic 1. 2. 3....

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Midterm today, 9pm Room 403 (bring your student id for entrance to the building)
Background image of page 2
13.9 Find a formula that is valid in all non- empty domains (hence simply valid) but not valid in an empty domain. ∀xPx => ∃xPx. In any non-empty domain, if all x is P, then there is x which is P. The formula is valid. In an empty domain, ∀xPx is vacuously true, but ∃xPx is false because there is no such x. The conditional is false in an empty domain.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Tautologies We can obtain a first-order formula X by substituting first-order formulas for the propositional variables in Y. Then X is an instance of a formula Y. Ex. If we substitute ∀xPx for p in pv~p, we obtain ∀xPx v ~∀xPx. A first-order formula is a tautology if it is an instance of a tautology of proposi-
Background image of page 4
However, not all valid formulas are tau- tologies. Exs. ∀x(Px v ~Px), ∀xPx => ∃xPx. T FX doesn’t close with eight tableaux rules in propositional logic. In order to prove valid formulas that are not tautologies, we need additional tableau rules for ∀ and ∃. tautolo- gies Valid formu- las
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Ex. proof of the formula ∀xPx => ∃xPx. (1) F∀xPx => ∃xPx
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/04/2010 for the course HSS Hss105 taught by Professor Yeelee during the Fall '09 term at Korea Advanced Institute of Science and Technology.

Page1 / 20

Logic1019 - Tableaux for first-order ]= logic 1. 2. 3....

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online