Skip to content

Research at St Andrews

Proof Analysis in Intermediate Logics

Research output: Contribution to journalArticle

DOI

Abstract

Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the explanation of the rules.
Close

Details

Original languageEnglish
Pages (from-to)71–92
Number of pages22
JournalArchive for Mathematical Logic
Volume51
Issue number1-2
DOIs
StatePublished - 2012

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. Intuitionistic decision procedures since Gentzen

    Dyckhoff, R. 5 May 2016 Advances in Proof Theory. Kahle, R., Strahm, T. & Studer, T. (eds.). Birkhäuser Basel, p. 245-267 (Progress in Computer Science and Applied Logic; vol. 28)

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

  2. POSIX lexing with derivatives of regular expressions (proof pearl)

    Ausaf, F., Dyckhoff, R. & Urban, C. 2016 Interactive Theorem Proving: 7th International Conference, ITP 2016, Nancy, France, August 22-25, 2016, Proceedings. Blanchette, J. C. & Merz, S. (eds.). Springer, p. 69-86 18 p. (Lecture Notes in Computer Science; vol. 9807)

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

  3. Some remarks on proof-theoretic semantics

    Dyckhoff, R. 2016 Advances in Proof-Theoretic Semantics. Piecha, T. & Schroeder-Heister, P. (eds.). Springer, p. 79-93 15 p. (Trends in Logic; vol. 43)

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

  4. Geometrisation of first-order logic

    Dyckhoff, R. & Negri, S. Jun 2015 In : Bulletin of Symbolic Logic. 21, 2, p. 123–163 41 p.

    Research output: Contribution to journalArticle

  5. Cut-elimination, substitution and normalisation

    Dyckhoff, R. 2015 Dag Prawitz on Proofs and Meaning. Wansing, H. (ed.). Springer, p. 163-187 (Outstanding Contributions to Logic; vol. 7)

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

Related by journal

  1. Decision methods for linearly ordered Heyting algebras

    Dyckhoff, R. & Negri, S. May 2006 In : Archive for Mathematical Logic. 45, 4, p. 411-422 12 p.

    Research output: Contribution to journalArticle

ID: 5106629