Skip to content

Research at St Andrews

A note on harmony

Research output: Contribution to journalArticle

Abstract

In the proof-theoretic semantics approach to meaning, harmony, requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony, requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony: imposes the existence of certain transformations of derivations, known as reduction and expansion. We propose a construction of the E-rules (in GE-form) from given I-rules, and prove that the constructed rules satisfy also local intrinsic harmony. The construction is based on a classification of I-rules, and constitute an implementation to Gentzen’s (and Prawitz’) remark, that E-rules can be “read off” I-rules.
Close

Details

Original languageEnglish
Pages (from-to)613–628
Number of pages16
JournalJournal of Philosophical Logic
Volume41
Issue number3
StatePublished - Jun 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. Truth, dependence and supervaluation: Living with the ghost

    Meadows, T. S. D. 2012 In : Journal of Philosophical Logic. [Online First], p. - 20 p.

    Research output: Contribution to journalArticle

  2. General-Elimination Harmony and the Meaning of the Logical Constants

    Read, S. L. 1 Oct 2010 In : Journal of Philosophical Logic. 39, 5, p. 557-576

    Research output: Contribution to journalArticle

  3. Ceteris Paribus Conditionals and Comparative Normalcy

    Smith, M. J. M. Feb 2007 In : Journal of Philosophical Logic. 36, 1, p. 97-121 25 p.

    Research output: Contribution to journalArticle

  4. What's wrong with Tonk(?)

    Cook, R. T. Apr 2005 In : Journal of Philosophical Logic. 34, 2, p. 217-226 10 p.

    Research output: Contribution to journalArticle

ID: 110395158