rules_mt

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

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

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