BCK-formulas having unique proofs

Sachio Hirokawa

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

3 Citations (Scopus)

Abstract

The set of relevantly balanced formulas is introduced in implicational fragment of BCK-logic. It is shown that any relevantly balanced formula has unique normal form proof. Such formulas are defined by the ‘relevance relation’ between type variables in a formula. The set of balanced formulas (or equivalently one-two-formulas) is included in the relevantly balanced formulas. The uniqueness of normal form proofs is known for balanced formulas as the coherence theorem. Thus the result extends the theorem with respect to implicational formulas. The set of relevantly balanced formulas is characterized as the set of irrelevant substitution instances of principal type-schemes of BCK-λ-terms.

Original languageEnglish
Title of host publicationCategory Theory and Computer Science, Proceedings
EditorsDavid H. Pitt, Pierre-Louis Curien, Samson Abramsky, Axel Poigne, David E. Rydeheard, Andrew M. Pitts
PublisherSpringer Verlag
Pages106-120
Number of pages15
ISBN (Print)9783540544951
DOIs
Publication statusPublished - Jan 1 1991
Event4th Biennial Summer Conference on Category Theory and Computer Science, 1991 - Paris, France
Duration: Sep 3 1991Sep 6 1991

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume530 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other4th Biennial Summer Conference on Category Theory and Computer Science, 1991
CountryFrance
CityParis
Period9/3/919/6/91

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Hirokawa, S. (1991). BCK-formulas having unique proofs. In D. H. Pitt, P-L. Curien, S. Abramsky, A. Poigne, D. E. Rydeheard, & A. M. Pitts (Eds.), Category Theory and Computer Science, Proceedings (pp. 106-120). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 530 LNCS). Springer Verlag. https://doi.org/10.1007/BFb0013460