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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Bibliographische Detailangaben

Hauptverfasser:	Baker, S. (VerfasserIn), Ireland, A. (VerfasserIn), Smaill, Alan (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Edinburgh 1991
Schriftenreihe:	University <Edinburgh> / Department of Artificial Intelligence: DAI research paper 560
Schlagworte:	Applied statistics, operational research Computer software Automatic theorem proving
Zusammenfassung:	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.
Beschreibung:	17 S.