{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Logic0923 - Knights and knaves w again 1 2 3 Tautologies...

This preview shows pages 1–6. Sign up to view the full content.

OE ° “± ±±± ±± Knights and knaves again 1. Tautologies, contradictions 2. Application of the symbolic method 3. NGP revisited

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

View Full Document
Errata in Ch.8 p. 56, 15 lines from bottom, Problem 8 .5 -> 1.5 p. 57, three lines below “NGP Revisited”: of -> if p. 59, 12 lines from bottom, Chapter 3 - > 2 p. 61, the last line, Problem 8 .2 -> 2.2 p. 64, 4 lines from bottom, the knight -> knave HW #3 is due 9/30 (Wed.)
Define a formula. 1. p, q, r, … are formulas. 2. If X and Y are formulas, then so are ~X, (X Y), (XvY), (X=>Y), (X±Y). 3. That’s it folks . (this is logicians’ expres- sion) Besides 1 & 2, there is no other way of making up a formula.

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

View Full Document
Three kinds of formulas Formulas that are not contradictions are called satisfiable (true-able). definitions e.g. abbrevi- ated Tautologies Always true (in every row) pv~ p t Contradic- tions Always false (in every row) p ∧∼ p f Contingent Neither t nor f pvq
Some tautologies ((p=>q) (q=>r))=>(p=>r), hypothetical syllogism (p (p=>q))=>q, modus ponens ((p=>q) ~q)=>~p, modus tollens ((~p=>q) (~p=>~q))=>p, reductio ad absurdum To show p, assume ~p and show that ~p implies both q and ~q (contradiction).

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}