Re: [tlaplus] Aside from WF and SF?

On Wed, Nov 12, 2025 at 11:34 PM Stephan Merz <stephan.merz@xxxxxxxxx> wrote:

As Andrew suspects, the second formula is equivalent to weak fairness:

THEOREM
ASSUME NEW ACTION A, NEW STATE v
PROVE WF_v(A) <=> [](<>[]ENABLED <<A>>_v => <><<A>>_v)
BY PTL

Stephan

On 13 Nov 2025, at 01:51, Andrew Helwer <andrew.helwer@xxxxxxxxx> wrote:

[](ENABLED <<A>>_v => <><<A>>_v) is equivalent to []((ENABLED A) ~> <><<A>>_v) which means if an A step is enabled (like at all), eventually it will be taken; moreover, it will also be taken after every time an A step is enabled in the future. This is like an even stronger fairness assumption, but looking through the texts I have it does not seem to be a standard one. The usual next strongest fairness assumption in temporal logic is unconditional fairness, which is just []<><<A>>_v. There are a lot of fairness definitions out there though so I'm sure someone has covered & named it.

For the second one, since P => <>P, it seems to be implied by weak fairness. So it is at most as strong as weak fairness. Is it any weaker than weak fairness? I can't think of how it could be, but then we should be able to rewrite it into weak fairness. And there I am somewhat at a loss.

Andrew

On Wed, Nov 12, 2025 at 4:09 PM Chris Ortiz <zitroomega@xxxxxxxxx> wrote:
Hello,

WF_v(A) == []([]ENABLED <<A>>_v => <><<A>>_v) and
SF_v(A) == []([]<>ENABLED <<A>>_v => <><<A>>_v)

Is there

[]( ENABLED <<A>>_v => <><<A>>_v) and
[](<>[]ENABLED <<A>>_v => <><<A>>_v ?

And what could they mean?

Thanks and best regards,
Chris (Zitro)

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