<p>I am reading the seminal paper &quot;On the temporal analysis of fairness&quot; by Gabbay, Pnueli, Shelah, Stavi, available at</p>
<p>shelah.logic.at/papers/134/</p>
<p>In Section 3, completeness of a set of axioms for LTL is established. I am struggling to prove the first (crucial) Lemma on page 172, which is basically unproven therein.(Same with many other statements in that section, but their proofs can be reconstructed.)
Does there exist an extended version of the above mentioned paper? Contacting the (still living) authors failed. Help would be appreciated.</p>

CC BY-SA 4.0
2022-09-07T17:31:26.317Z
Don't read ancient papers. If you are looking for a modern treatment of some results on temporal logic, consult an appropriate handbook or a book on temporal logics. A good reference list is available here: https://www.mimuw.edu.pl/~vbarany/TL_course.html
Bartosz Bednarczyk
CC BY-SA 4.0
2022-09-07T18:13:57.473Z
Ironically, one of the references in the list of papers suggested by B. Bednarczyk is "The temporal analysis of fairness" (an "ancient" but seminal paper.....). None of the others seems to address in detail the completeness issue of LTL.
sbarra
CC BY-SA 4.0
2022-09-07T19:01:48.113Z
What kind of result are you looking for? Expressive completeness of LTL? It's not clear from your question. You may also check the slides: https://www.cmi.ac.in/~kumar/words/LTLSlides.pdf
Bartosz Bednarczyk
CC BY-SA 4.0
2022-09-08T06:02:25.867Z
This paper is indeed particularly hard to read. Can you perhaps distill exactly what you're trying to prove, i.e., the necessary definitions and claims? (so that people don't have to go through the whole thing).
Also, perhaps this would be relevant: https://dl.acm.org/doi/fullHtml/10.1145/3387109
Shaull
CC BY-SA 4.0
2022-09-08T16:40:48.217Z
Yes, the paper is not so easy to read: proofs are just sketched, at best.  Incidentally,  the paper has received more that 1100 citations (and it is written by 4 leading logicians/computer_scientists),  Providing the necessary definitions and claims requires providing the content of the entire section 3. I am interested in the proof of a  lemma because I would like to prove a similar result in a different framework. Hence my question is very specific. Unfortunately, general references are not helpful.
sbarra
CC BY-SA 4.0
2022-09-09T04:59:25.173Z
@sbarra if you write down what you're trying to prove, perhaps it would be easier for us to have a look.
Shaull
<lo.logic>
On completeness of LTL
sbarra
# On completeness of LTL

(Asked by: username_0 on 2022-09-07)

I am reading the seminal paper "On the temporal analysis of fairness" by Gabbay, Pnueli, Shelah, Stavi, available at

shelah.logic.at/papers/134/

In Section 3, completeness of a set of axioms for LTL is established. I am struggling to prove the first (crucial) Lemma on page 172, which is basically unproven therein.(Same with many other statements in that section, but their proofs can be reconstructed.)
Does there exist an extended version of the above mentioned paper? Contacting the (still living) authors failed. Help would be appreciated.

**Tags:** lo.logic

> **Comments:**
> **username_1**: Don't read ancient papers. If you are looking for a modern treatment of some results on temporal logic, consult an appropriate handbook or a book on temporal logics. A good reference list is available here: https://www.mimuw.edu.pl/~vbarany/TL_course.html  
> **username_0**: Ironically, one of the references in the list of papers suggested by B. Bednarczyk is "The temporal analysis of fairness" (an "ancient" but seminal paper.....). None of the others seems to address in detail the completeness issue of LTL.  
> **username_1**: What kind of result are you looking for? Expressive completeness of LTL? It's not clear from your question. You may also check the slides: https://www.cmi.ac.in/~kumar/words/LTLSlides.pdf  
> **username_2**: This paper is indeed particularly hard to read. Can you perhaps distill exactly what you're trying to prove, i.e., the necessary definitions and claims? (so that people don't have to go through the whole thing). Also, perhaps this would be relevant: https://dl.acm.org/doi/fullHtml/10.1145/3387109  
> **username_0**: Yes, the paper is not so easy to read: proofs are just sketched, at best.  Incidentally,  the paper has received more that 1100 citations (and it is written by 4 leading logicians/computer_scientists),  Providing the necessary definitions and claims requires providing the content of the entire section 3. I am interested in the proof of a  lemma because I would like to prove a similar result in a different framework. Hence my question is very specific. Unfortunately, general references are not helpful.  
> **username_2**: @username_0 if you write down what you're trying to prove, perhaps it would be easier for us to have a look.  

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## 0 answers

