On the use of the constructive omega-rule within automated deduction:
Abstract: "The cut elimination theorem for predicate calculus states that every proof may be replaced by one which does not involve use of the cut rule. This theorem no longer holds when the system is extended with Peano's axioms to give a formalisation for arithmetic. The problem of gener...
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Edinburgh
1991
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| Series: | University <Edinburgh> / Department of Artificial Intelligence: DAI research paper
560 |
| Subjects: | |
| Summary: | Abstract: "The cut elimination theorem for predicate calculus states that every proof may be replaced by one which does not involve use of the cut rule. This theorem no longer holds when the system is extended with Peano's axioms to give a formalisation for arithmetic. The problem of generalisation results, since arbitrary formulae can be cut in. This makes theorem-proving very difficult -- one solution is to embed arithmetic in a stronger system, where cut elimination holds. In particular, this is the case given the addition of the constructive w-rule: if each P(n) can be proved in a uniform way (from parameter n), then conclude [for all]nP(n) This paper describes a system basaed on this rule, and shows that certain statements are provable in this system which are not provable in Peano arithmetic without cut. Moreover, an important application is presented in the form of a new method of generalisation by means of 'guiding proofs' in the stronger system, which sometimes succeeds in producing proofs in the original system when other methods fail. The implementation of such a system is also described. |
| Physical Description: | 17 S. |
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| 245 | 1 | 0 | |a On the use of the constructive omega-rule within automated deduction |c S. Baker ; A. Ireland ; A. Smaill |
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| 490 | 1 | |a University <Edinburgh> / Department of Artificial Intelligence: DAI research paper |v 560 | |
| 520 | 3 | |a Abstract: "The cut elimination theorem for predicate calculus states that every proof may be replaced by one which does not involve use of the cut rule. This theorem no longer holds when the system is extended with Peano's axioms to give a formalisation for arithmetic. The problem of generalisation results, since arbitrary formulae can be cut in. This makes theorem-proving very difficult -- one solution is to embed arithmetic in a stronger system, where cut elimination holds. In particular, this is the case given the addition of the constructive w-rule: if each P(n) can be proved in a uniform way (from parameter n), then conclude [for all]nP(n) | |
| 520 | 3 | |a This paper describes a system basaed on this rule, and shows that certain statements are provable in this system which are not provable in Peano arithmetic without cut. Moreover, an important application is presented in the form of a new method of generalisation by means of 'guiding proofs' in the stronger system, which sometimes succeeds in producing proofs in the original system when other methods fail. The implementation of such a system is also described. | |
| 650 | 7 | |a Applied statistics, operational research |2 sigle | |
| 650 | 7 | |a Computer software |2 sigle | |
| 650 | 4 | |a Automatic theorem proving | |
| 700 | 1 | |a Ireland, A. |e Verfasser |4 aut | |
| 700 | 1 | |a Smaill, Alan |e Verfasser |4 aut | |
| 810 | 2 | |a Department of Artificial Intelligence: DAI research paper |t University <Edinburgh> |v 560 |w (DE-604)BV010450646 |9 560 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006968056 | |
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| id | DE-604.BV010458953 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-15T10:07:52Z |
| institution | BVB |
| language | English |
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| physical | 17 S. |
| publishDate | 1991 |
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| series2 | University <Edinburgh> / Department of Artificial Intelligence: DAI research paper |
| spelling | Baker, S. Verfasser aut On the use of the constructive omega-rule within automated deduction S. Baker ; A. Ireland ; A. Smaill Edinburgh 1991 17 S. txt rdacontent n rdamedia nc rdacarrier University <Edinburgh> / Department of Artificial Intelligence: DAI research paper 560 Abstract: "The cut elimination theorem for predicate calculus states that every proof may be replaced by one which does not involve use of the cut rule. This theorem no longer holds when the system is extended with Peano's axioms to give a formalisation for arithmetic. The problem of generalisation results, since arbitrary formulae can be cut in. This makes theorem-proving very difficult -- one solution is to embed arithmetic in a stronger system, where cut elimination holds. In particular, this is the case given the addition of the constructive w-rule: if each P(n) can be proved in a uniform way (from parameter n), then conclude [for all]nP(n) This paper describes a system basaed on this rule, and shows that certain statements are provable in this system which are not provable in Peano arithmetic without cut. Moreover, an important application is presented in the form of a new method of generalisation by means of 'guiding proofs' in the stronger system, which sometimes succeeds in producing proofs in the original system when other methods fail. The implementation of such a system is also described. Applied statistics, operational research sigle Computer software sigle Automatic theorem proving Ireland, A. Verfasser aut Smaill, Alan Verfasser aut Department of Artificial Intelligence: DAI research paper University <Edinburgh> 560 (DE-604)BV010450646 560 |
| spellingShingle | Baker, S. Ireland, A. Smaill, Alan On the use of the constructive omega-rule within automated deduction Applied statistics, operational research sigle Computer software sigle Automatic theorem proving |
| title | On the use of the constructive omega-rule within automated deduction |
| title_auth | On the use of the constructive omega-rule within automated deduction |
| title_exact_search | On the use of the constructive omega-rule within automated deduction |
| title_full | On the use of the constructive omega-rule within automated deduction S. Baker ; A. Ireland ; A. Smaill |
| title_fullStr | On the use of the constructive omega-rule within automated deduction S. Baker ; A. Ireland ; A. Smaill |
| title_full_unstemmed | On the use of the constructive omega-rule within automated deduction S. Baker ; A. Ireland ; A. Smaill |
| title_short | On the use of the constructive omega-rule within automated deduction |
| title_sort | on the use of the constructive omega rule within automated deduction |
| topic | Applied statistics, operational research sigle Computer software sigle Automatic theorem proving |
| topic_facet | Applied statistics, operational research Computer software Automatic theorem proving |
| volume_link | (DE-604)BV010450646 |
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