Balanced formulas, BCK-minimal formulas and their proofs

Sachio Hirokawa

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

    3 Citations (Scopus)


    The structure of normal form proof figures are investigated for implicatonal formulas in BCK-logic, in which each assumption can be used at most once. Proof figures are identified with λ-terms. A formula is balanced iff no type variable occurs more than twice in it. It is known that proof figure in βη-normal is unique for balanced formulas. In this paper, it is shown that closed λ-terms in β-normal form having balanced types are BCK-λ-terms in which each variable occurs at most once. A formula is BCK-minimal iff it is BCK-provable and it is not a non-trivial substitution instance of other BCK-provable formula. It is also shown that the set BCK-minimal formulas is identical to the set of principal type-schemes of BCK-λ-terms in βη-normal form.

    Original languageEnglish
    Title of host publicationLogical Foundations of Computer Science — Tver 1992 - 2nd International Symposium, Proceedings
    EditorsAnil Nerode, Mikhail Taitslin
    PublisherSpringer Verlag
    Number of pages11
    ISBN (Print)9783540557074
    Publication statusPublished - 1992
    Event2nd International Symposia on Logical Foundations of Computer Science, Tver 1992 - Tver, Russian Federation
    Duration: Jul 20 1992Jul 24 1992

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume620 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349


    Other2nd International Symposia on Logical Foundations of Computer Science, Tver 1992
    Country/TerritoryRussian Federation

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)


    Dive into the research topics of 'Balanced formulas, BCK-minimal formulas and their proofs'. Together they form a unique fingerprint.

    Cite this