rules_mt - The Natural Deduction Rules and Truth-Table...

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

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

Unformatted text preview: The Natural Deduction Rules and Truth-Table Definitions (Mid-Term) Rule of Assumptions: j (j) p Assumption (or: Premise) Rule of Double Negation (DN): a1 ,. . . , an a1 ,. . . , an (j) . . . (k) p p j DN where p may be any formula. Rule of &-Elimination (&E): a1 ,. . . , an a1 ,. . . , an (j) . . . (k) p&q p (or q) j &E Rule of -Introduction (I): a1 ,. . . , an a1 ,. . . , an a1 ,. . . , an (j) . . . (k) or (k) p pq qp j I j I Rule of &-Introduction (&I): a1 ,. . . , an b1 ,. . . , bu a1 ,. . . , an , b1 ,. . . , bu (j) . . . (k) . . . (m) p q p&q j, k &I Rule of -Elimination (E): a1 ,. . . , an h b1 ,. . . , bu j (g) . . . (h) . . . (i) . . . (j) . . . (k) . . . (m) pq p r q r r g, h, i, j, k E Assumption Assumption Rule of -Elimination (E): a1 ,. . . , an b1 ,. . . , bu a1 ,. . . , an , b1 ,. . . , bu (j) . . . (k) . . . (m) pq p q j, k E c1 ,. . . , cw A A = {a1 ,. . . , an } {b1 ,. . . , bu }/h {c1 ,. . . , cw }/j p p Assumption p q p&q pq Rule of -Introduction (I): j a1 ,. . . , an {a1 ,. . . , an }/j (j) . . . (k) . . . (m) p q pq j, k I p (j) . . . (k) . . . (m) q q j, k E Rule of -Introduction (I): j a1 ,. . . , an {a1 ,. . . , an }/j (j) . . . (k) . . . (m) p Assumption p q p j, k I p q q Rule of -Elimination (E): a1 ,. . . , an b1 ,. . . , bu a1 ,. . . , an , b1 ,. . . , bu pq pq ...
View Full Document

This note was uploaded on 09/23/2009 for the course PHIL 12A taught by Professor Fitelson during the Spring '08 term at Berkeley.

Ask a homework question - tutors are online