Murdoch J. Gabbay - The language of Stratified Sets is confluent and strongly normalising

lmcs:3681 - Logical Methods in Computer Science, May 23, 2018, Volume 14, Issue 2 - https://doi.org/10.23638/LMCS-14(2:12)2018
The language of Stratified Sets is confluent and strongly normalisingArticle

Authors: Murdoch J. Gabbay ORCID

    We study the properties of the language of Stratified Sets (first-order logic with $\in$ and a stratification condition) as used in TST, TZT, and (with stratifiability instead of stratification) in Quine's NF. We find that the syntax forms a nominal algebra for substitution and that stratification and stratifiability imply confluence and strong normalisation under rewrites corresponding naturally to $\beta$-conversion.

    https://doi.org/10.23638/LMCS-14(2:12)2018
    Source: arXiv.org:1705.07767
    Volume: Volume 14, Issue 2
    Published on: May 23, 2018
    Accepted on: April 19, 2018
    Submitted on: May 23, 2017
    Keywords: Computer Science - Logic in Computer Science,D.3.1,F.3.2,F.4.1
    Licence: Attribution 4.0 International (CC BY 4.0)

    Classifications

    Mathematics Subject Classification 20201
    Sources:
    • [1] zbMATH Open.

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