St Andrews Research Repository

St Andrews University Home
View Item 
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.

Cut-elimination, substitution and normalisation

Thumbnail
View/Open
cutreduction.pdf (160.7Kb)
Date
2015
Author
Dyckhoff, Roy
Keywords
Intuitionistic logic
Minimal logic
Sequent calculus
Natural deduction
Cut-elimination
Substitution
Normalisation
QA75 Electronic computers. Computer science
BC Logic
Metadata
Show full item record
Altmetrics Handle Statistics
Altmetrics DOI Statistics
Abstract
We present a proof (of the main parts of which there is a formal version, checked with the Isabelle proof assistant) that, for a G3-style calculus covering all of intuitionistic zero-order logic, with an associated term calculus, and with a particular strongly normalising and confluent system of cut-reduction rules, every reduction step has, as its natural deduction translation, a sequence of zero or more reduction steps (detour reductions, permutation reductions or simplifications). This complements and (we believe) clarifies earlier work by (e.g.) Zucker and Pottinger on a question raised in 1971 by Kreisel.
Citation
Dyckhoff , R 2015 , Cut-elimination, substitution and normalisation . in H Wansing (ed.) , Dag Prawitz on Proofs and Meaning . Outstanding Contributions to Logic , vol. 7 , Springer , pp. 163-187 . https://doi.org/10.1007/978-3-319-11041-7_7
Publication
Dag Prawitz on Proofs and Meaning
Status
Peer reviewed
DOI
https://doi.org/10.1007/978-3-319-11041-7_7
ISSN
2211-2758
Type
Book item
Rights
© Springer International Publishing Switzerland 2015. The final publication is available at link.springer.com
Description
Date of Acceptance: 01/2015
Collections
  • University of St Andrews Research
URI
http://hdl.handle.net/10023/7962

Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.

Advanced Search

Browse

All of RepositoryCommunities & CollectionsBy Issue DateNamesTitlesSubjectsClassificationTypeFunderThis CollectionBy Issue DateNamesTitlesSubjectsClassificationTypeFunder

My Account

Login

Open Access

To find out how you can benefit from open access to research, see our library web pages and Open Access blog. For open access help contact: openaccess@st-andrews.ac.uk.

Accessibility

Read our Accessibility statement.

How to submit research papers

The full text of research papers can be submitted to the repository via Pure, the University's research information system. For help see our guide: How to deposit in Pure.

Electronic thesis deposit

Help with deposit.

Repository help

For repository help contact: Digital-Repository@st-andrews.ac.uk.

Give Feedback

Cookie policy

This site may use cookies. Please see Terms and Conditions.

Usage statistics

COUNTER-compliant statistics on downloads from the repository are available from the IRUS-UK Service. Contact us for information.

© University of St Andrews Library

University of St Andrews is a charity registered in Scotland, No SC013532.

  • Facebook
  • Twitter