|
A formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language) each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference. The last sentence in the sequence is a theorem of a formal system. The notion of theorem is not in general effective, therefore there may be no method by which we can always find a proof of a given sentence or determine that none exists. The concept of natural deduction is a generalization of the concept of proof. The theorem is a syntactic consequence of all the well-formed formulas preceding it in the proof. For a well-formed formula to qualify as part of a proof, it must be the result of applying a rule of the deductive apparatus of some formal system to the previous well-formed formulae in the proof sequence. Formal proofs often are constructed with the help of computers in interactive theorem proving. Significantly, these proofs can be checked automatically, also by computer. Checking formal proofs is usually simple, whereas finding proofs (automated theorem proving) is generally computationally hard. BackgroundFrom Wikipedia under the
GNU Free Documentation License From Yahoo Image Search: "formal proof"  redreporter.com Slyde ue, 16 Jun 2009 21:00:20 GM He had to stay at second. because the CF very nearly caught it. As it, he dove and it popped out of his glove. Let me write out a . formal proof. for you. by Gray on Jun 16, 2009 7:33 PM EDT to parent up reply actions 0 recs ...  topviewed.info sruthin Sat, 11 Jul 2009 11:25:00 GM The chapters in this book deal with: The benefits and technical challenges of sharing . formal. mathematics among interactive theorem provers; . proof. normalization for various axiomatic theories; abstraction-refinement framework of temporal ...  witsendnj.blogspot.com Gail Sat, 11 Jul 2009 13:04:00 GM While they lived there, the . formal. gardens were installed with stone walls, walks, delightful bridges and stepped ponds, statuary and gates and trellises. Many, many exotic and indigenous trees and shrubs were planted throughout the ... From Google Blog Search: "formal proof"  news.google.com The Gazette (Montreal) During an election campaign, after all, any claims without engraved-on-granite proof must be handled cautiously. Still, what we know for certain - conflicts ... and more » news.google.com Winnisquam Echo Franson asked if the trash receptacles would be bear proof , a request that Lief said would be granted. Pope received assurance that there would be an ... and more » news.google.com guardian.co.uk Under Swiss law, the US has 60 days to file a formal extradition request. That request must be examined by the justice ministry, and if approved can be ... and more » From Google News Search: "formal proof" Construct a formal proof of validity to show that the conclusion of this passage is true.? Q. If passenger Jones is the brakeman s next-door neighbor, then passenger Jones s annual earnings are exactly divisible by 3. If passenger Jones s annual earnings are exactly divisible by 3, then $40K is exactly divisible by 3. But $40K is not exactly divisible by 3. If passenger Robinson is the brakeman s next-door neighbor, then passenger Robinson lives halfway between Detroit and Chicago. If passenger Robinson lives in Detroit, then he does not live halfway between Detroit and Chicago. Passenger Robinson lives in Detroit. If passenger Jones is not the brakeman s next-door neighbor, then either passenger Robinson or passenger Smith is the brakeman s next-door neighbor. Therefore, passenger Smith is the brakeman s next-door neighbor. … [cont.] Asked by yahschild2000 - Sun Dec 14 22:12:38 2008 - - 1 Answers - 0 Comments A. If X then Y usually means X implies Y. So we reduce the passage to the following database. I'll number the rules for reference. (1) J implies E (2) E implies T (3) not T (4) R implies H (5) D implies not H (6) D (7) not J implies (R or S) Modus ponens (MP) is a rule that works as follows. If you know A implies B, and you know A is true, then you may conclude B is true and add it to your database. Modus tollens (MT) is a rule that works as follows. If you know A implies B, and you know B is false (not B), then you may conclude A is false (not A) and add it to your database. Here we go. (2) E implies T (3) not T (8) therefore, by MT, not E (1) J implies E (8) not E (9) therefore, by MT, not J (7) not J implies (R or S) (9) not J (1 [cont.] Answered by Stacy P - Wed Dec 17 13:29:38 2008 Define how 2 use a formal proof 2 show that a set of statements is inconsistant.? Q. Define how 2 use a formal proof 2 show that a set of statements is inconsistant.? Asked by *Daisy* - Wed Nov 19 09:33:08 2008 - - 2 Answers - 0 Comments A. This is rather a vague question but I'll have a go. Suppose you have a set of three statments A, B, C. You could prove that any two e.g. A and B together imply the opposite of C. You could prove that all three together lead to an absurdity like 1 = 0. You could show that any two are directly contradictory. That's the best I can do without a definite context. Answered by mathsmanretired - Wed Nov 19 09:54:05 2008 Write a formal proof of the theorem.?
Q. The diagonals of a square are perpendicular. Asked by Cat - Mon Feb 12 00:14:45 2007 - - 3 Answers - 0 Comments A. Angus gave a proof out of analytical geometry. Not bad. Sometimes it isn't clear what the ground rules are; I'll give you another proof that doesn't use coordinates (although Angus' will be easier to read, I think). Call the vertices A, B, C, and D as you go around the square; let E be the point of intersection of the diagonals. Since ABCD is a square, AB=BC=CD=AD and angles ABC, BCD, CDA, and DAB are all right angles. This means that triangles ACD and BCD are isosceles right triangles (45-45-90), so angles BDC and ACD are each 45 degrees. Those two angles are also known by the names EDC and ECD. Since the interior angles of a triangle add up to 180 degrees, this means that angle CED is a right angle, so the diagonals are… [cont.] Answered by Doc B - Mon Feb 12 00:47:00 2007 From Yahoo Answer Search: "formal proof" |
