Normalization, Cut-Elimination, and the Theory of Proofs (Center for the Study of Language and Information - Lecture Notes)

A. M. Ungar

ISBN 10: 0937073822 / ISBN 13: 9780937073827

Editore: Center for the Study of Language and Inf, 1992

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Codice articolo ZB1315601

Dati bibliografici

• Titolo: Normalization, Cut-Elimination, and the Theory of Proofs (Center for the Study of Language and Information - Lecture Notes)
• Editore: Center for the Study of Language and Inf
• Data di pubblicazione: 1992
• Lingua: Inglese
• ISBN 10: 0937073822
• ISBN 13: 9780937073827
• Rilegatura: Brossura
• Condizione: Very Good

Descrizione articolo

Riassunto

Gentzen's cut-elimination theorem is widely used as a tool for meta-mathematical investigations. It is sometimes claimed however that the theorem and its proof have interest which is independent of these applications and derives from the information they supply about the structure of proofs in general. Ungar investigates this claim in the context of first order logic. Ungar gives an account of Gentzen's theorem for various formalisms and discusses the difficulties involved in treating these different versions uniformly, as instances of a single theorem which is not tied to a particular system of rules. By extending the theorem to a natural deduction calculus whose derivations are allowed to have more than one conclusion, Ungar argues that the different versions of the theorem are more or less natural specializations of a single result whose significance can be understood in terms of the proofs represented by formal derivations. A concluding discussion focuses on the relationship between proofs and formal derivations, and the role proofs may play as part of a general theory of evidence.

Contenuti

Introduction; 1. Background; 2. Comparing NJ with LJ; 3. Natural deduction revisited; 4. The problem of substitution; 5. A multiple-conclusion calculus; 6. Reduction procedures; 7. Correspondence results; 8. Interpretations of derivations; Appendices; Index.