# A separation theorem for discrete-time interval temporal logic

A separation theorem for discrete-time interval temporal logic Gabbay's separation theorem about linear temporal logic with past has proved to be one of the most useful theoretical results in temporal logic. In this paper, we establish an analogous statement about Moszkowski's discrete-time propositional Interval Temporal Logic ( ) with two sets of expanding modalities, namely the unary neighbourhood modalities and the binary weak inverses of 's chop operator. We prove that separation holds for both with and without its loop construct chop-star. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Non-Classical Logics Taylor & Francis

# A separation theorem for discrete-time interval temporal logic

, Volume 32 (1): 27 – Jan 2, 2022
27 pages

## A separation theorem for discrete-time interval temporal logic

Abstract

Gabbay's separation theorem about linear temporal logic with past has proved to be one of the most useful theoretical results in temporal logic. In this paper, we establish an analogous statement about Moszkowski's discrete-time propositional Interval Temporal Logic ( ) with two sets of expanding modalities, namely the unary neighbourhood modalities and the binary weak inverses of 's chop operator. We prove that separation holds for both with and without its loop construct...

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Publisher
Taylor & Francis
ISSN
1958-5780
eISSN
1166-3081
DOI
10.1080/11663081.2022.2050135
Publisher site
See Article on Publisher Site

### Abstract

Gabbay's separation theorem about linear temporal logic with past has proved to be one of the most useful theoretical results in temporal logic. In this paper, we establish an analogous statement about Moszkowski's discrete-time propositional Interval Temporal Logic ( ) with two sets of expanding modalities, namely the unary neighbourhood modalities and the binary weak inverses of 's chop operator. We prove that separation holds for both with and without its loop construct chop-star.

### Journal

Journal of Applied Non-Classical LogicsTaylor & Francis

Published: Jan 2, 2022

Keywords: Gabbay separation; interval temporal logic; expanding modalities

### References

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