The language of Stratified Sets is confluent and strongly normalising

Murdoch J. Gabbay

doi:10.23638/LMCS-14(2:12)2018

The language of Stratified Sets is confluent and strongly normalising

Murdoch J. Gabbay

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Abstract

We study the properties of the language of Stratified Sets (first-order logic with ∈ 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 β-conversion.

Original language	English
Article number	12
Journal	Logical Methods in Computer Science
Volume	14
Issue number	2
DOIs	https://doi.org/10.23638/LMCS-14(2:12)2018
Publication status	Published - 22 May 2018

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AB - We study the properties of the language of Stratified Sets (first-order logic with ∈ 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 β-conversion.

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The language of Stratified Sets is confluent and strongly normalising

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