Dijkstra notation in physics or statistics

[bjbr...@gmail.com]

Hello All,

In the privacy of my own scribbling I am comfortable using Dijkstra's bracket notation and other conventions of the Calculus of Boolean Structures, but I haven't used it or seen it used in published work in physical science or applied statistics. But I just put a manuscript on Arxiv that uses the conventions extensively.

Estimating the Missing Mass, Partition Function or Evidence for a Case of Sampling from a Discrete Set

https://arxiv.org/abs/2603.13207

See the Section on Notation and the Appendix with Remarks on Notation, and of course all the manuscript for its application. The work needs some further development before it goes to a journal, and I have no idea how much the notation will be an issue.

Comments will be appreciated, and I will certainly appreciate to know of precedent for Dijkstra's notation in physics or statistics literature.

Bas Braams

[Diethard Michaelis]

Hi Bas,

My comments (sorry for being so late ...):

(0) "Dijkstra’s bracket notation"
is usually known as
"Eindhoven quantifier notation".
It might be useful to have a look in the books/writings of others using
Eindhoven notation [and calculational proof (Feijen proof format)].
I'd suggest Roland Backhouse for a very first try.

(1) For "bracket" see e.g. https://en.wikipedia.org/wiki/Bracket.
"bracket" is used for "square bracket", not "angle bracket".
But I'm not a native English speaker.

(2) The everywhere operator [P] might be best described by

[P] := (P = true), i.e. "P equals true".

This way [] is defined for any Boolean algebra.
Describing it as universal quantification over some obscure state space
is just a special case of (= true).

(3) The = symbol is indeed best used for "complete equality".
Even Dijkstra had some doubts with his "lifted" = ,
see the end of EWD 1300.

(4) EWD1300: "The Notational Conventions I Adopted, and Why"
https://www.cs.utexas.edu/~EWD/transcriptions/EWD13xx/EWD1300.html
is more up to date on notation than the Dijkstra/Scholten book.
It is published in
Formal Aspects of Computing, Vol. 14, No. 2
https://doi.org/10.1007/s001650200030

(5) Boolean "structure"
for "element of a Boolean algebra"
seems to be quite uncommon outside Dijkstra's writings.
It somehow conflicts with the standard use of "structure"
and so it does in your paper.
I think there is even a comment by Dijkstra on it
suggesting a different terminology,
but I don't remember where nor what he suggested ...

Cheers,
Happy Easter Days,
Diethard.

[Kevin]

Hi.

(5) Boolean "structure"
for "element of a Boolean algebra"
seems to be quite uncommon outside Dijkstra's writings.
It somehow conflicts with the standard use of "structure"
and so it does in your paper.
I think there is even a comment by Dijkstra on it
suggesting a different terminology,
but I don't remember where nor what he suggested ...

At the bottom of EWD1086-2, he suggests the name "profiles".

Best regards

Kevin