RE: [ontolog-forum] symbolic equation?

OpenMath represents all mathematical expressions as trees (there is scope for DAGs, but this is really just space optimisation at one level), including equations.  Note that many people would represent a=b as
    =
/    \
a     b
OpenMath represents it as
      OMA   (OpenMath application)
   /   |   \
=     a     b
= is a node of type OMS (OpenMath symbol) with defined semantics
a and b are nodes of type OMV (OpenMath variable).
This way the unbounded variety of mathematical notation can be represented in a fixed number of node types.
James
From: ontolog-forum@googlegroups.com <ontolog-forum@googlegroups.com> On Behalf Of Paola Di Maio
Sent: 28 June 2020 00:25
To: ontolog-forum <ontolog-forum@googlegroups.com>
Cc: W3C AIKR CG <public-aikr@w3.org>
Subject: Re: [ontolog-forum] symbolic equation?

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Thank you Alex
as per my reply to John- it looks like the paper you point to also uses symbolic as in alphanumeric
algebra
(the question originated from a symbolic KR point of view which is something else entirely, I now start thinking the use of the term symbolic should be better disambiguated)  symbolic AI/KR is not related to
algebraic notation, afaik

anyway, I love the representation of equations as trees. I need to try that out, maybe write an exercise book to transform equations into trees, and vice versa,  But from my guess. not every equation can be translated to a tree, what do you think?

It will take also an awful lot of space. I still like trees much more than I like equations

PDM

On Sun, Jun 28, 2020 at 12:32 AM Alex Shkotin <alex.shkotin@gmail.com<mailto:alex.shkotin@gmail.com>> wrote:
I got it https://groups.google.com/d/msg/ontolog-forum/MuVb2mRSACc/E2oX4krcAAAJ<https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgroups.google.com%2Fd%2Fmsg%2Fontolog-forum%2FMuVb2mRSACc%2FE2oX4krcAAAJ&data=02%7C01%7Cmasjhd%40bath.ac.uk%7C30f92a448331427b842608d81af15969%7C377e3d224ea1422db0ad8fcc89406b9e%7C0%7C0%7C637288972359382989&sdata=uMaQ8%2Fjn3qY9THWxMI1KM0568F0mlFzn%2Fg1ImVo3DJE%3D&reserved=0>

сб, 27 июн. 2020 г. в 15:23, Paola Di Maio <paola.dimaio@gmail.com<mailto:paola.dimaio@gmail.com>>:
Yes I think I am seeing that
Please share exciting examples

On Sat, Jun 27, 2020 at 8:16 PM Alex Shkotin <alex.shkotin@gmail.com<mailto:alex.shkotin@gmail.com>> wrote:
Paola,

I absolutely agree with your intention and my way would be to get from the authors definitions for both:-)
But I am in the position that most important and even terrific is that they begin to train ANN with symbolic input and/or output, getting exciting results.

сб, 27 июн. 2020 г. в 14:50, Paola Di Maio <paola.dimaio@gmail.com<mailto:paola.dimaio@gmail.com>>:
James
good read, thanks for sharing
well, I am familiar with equations in algebra, but did not know the other meanings, so I definitely learn something :-)
Alex:   I am only concerned with ambiguity/misuse/undefined/misleading  terminology
In KR, afaik, symbolic representation does not include algebra, but some scholars include in symbolic representation some types of logical notation or techniques such as baesyan inference which uses algebraic notation.  Would his symbolic equation mean this is symbolic representation (in which case I would disagree/not be sure/have to look further into it) would this symbolic equation mean something else,
in a mathematical sense (this is why I asked)   if so why does it not exist in the encyclopedia of mathematics which is what I look up from time to time as a reference
If its just used as a colloqualism to mean symbolic expression then note that even that does not exist
as a term itself,(many forms of expression in algebra but symbolic expression is not a formal definition according to the encyclopedia)  I am being pedantic only because I d like to understand what people are talking about with these equations
https://encyclopediaofmath.org/index.php?search=%22+expression%22&title=Special%3ASearch&profile=default&fulltext=1<https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fencyclopediaofmath.org%2Findex.php%3Fsearch%3D%2522%2Bexpression%2522%26title%3DSpecial%253ASearch%26profile%3Ddefault%26fulltext%3D1&data=02%7C01%7Cmasjhd%40bath.ac.uk%7C30f92a448331427b842608d81af15969%7C377e3d224ea1422db0ad8fcc89406b9e%7C0%7C0%7C637288972359382989&sdata=gKJ8aoF8vjaWYo66%2FxXE8Pv5iqPj7WpKnj9jC9qaZUg%3D&reserved=0>

On Sat, Jun 27, 2020 at 6:51 PM 'James Davenport' via ontolog-forum <ontolog-forum@googlegroups.com<mailto:ontolog-forum@googlegroups.com>> wrote:
There is also significant ambiguity over the meaning of the word ‘equation’: see
Marcus,S. & Watt,S.M.,
What is an Equation?.
Proc. SYNASC 2012, IEEE Press, 2012, pp. 23-29,
http://www.csd.uwo.ca/~watt/pub/reprints/2012-synasc-equations.pdf<https://eur01.safelinks.protection.outlook.com/?url=http:%2F%2Fwww.csd.uwo.ca%2F~watt%2Fpub%2Freprints%2F2012-synasc-equations.pdf&data=02%7C01%7Cmasjhd%40bath.ac.uk%7C30f92a448331427b842608d81af15969%7C377e3d224ea1422db0ad8fcc89406b9e%7C0%7C0%7C637288972359392986&sdata=37MshRFSgLrL38Wa%2FS9QGKLYOX6Wa0niLM2awQZXREg%3D&reserved=0>

From: ontolog-forum@googlegroups.com<mailto:ontolog-forum@googlegroups.com> <ontolog-forum@googlegroups.com<mailto:ontolog-forum@googlegroups.com>> On Behalf Of Alex Shkotin
Sent: 27 June 2020 11:09
To: ontolog-forum <ontolog-forum@googlegroups.com<mailto:ontolog-forum@googlegroups.com>>
Cc: W3C AIKR CG <public-aikr@w3.org<mailto:public-aikr@w3.org>>
Subject: Re: [ontolog-forum] symbolic equation?

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By the way in the paper itself there is no term "symbolic equation" the most used is "symbolic expression".

сб, 27 июн. 2020 г. в 12:05, Paola Di Maio <paola.dimaio@gmail.com<mailto:paola.dimaio@gmail.com>>:
yes, I could not find any reference in the history of maths to symbolic equations
as constructs


On Sat, Jun 27, 2020 at 4:53 PM Alex Shkotin <alex.shkotin@gmail.com<mailto:alex.shkotin@gmail.com>> wrote:
Paola,

Are you asking specifically about this particular symbolic equation?
[image.png]

Alex

сб, 27 июн. 2020 г. в 02:41, Paola Di Maio <paola.dimaio@gmail.com<mailto:paola.dimaio@gmail.com>>:
I  am not sure I understand the construct symbolic equation in this slide
anyone could like to comment/explain?
https://twitter.com/ykilcher/status/1276158135258972161/photo/1<https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Ftwitter.com%2Fykilcher%2Fstatus%2F1276158135258972161%2Fphoto%2F1&data=02%7C01%7Cmasjhd%40bath.ac.uk%7C30f92a448331427b842608d81af15969%7C377e3d224ea1422db0ad8fcc89406b9e%7C0%7C0%7C637288972359392986&sdata=IYy%2BdROlCVJ8%2BVOlbt9lcSkwhNWLL6TnVc%2BJPGN8e14%3D&reserved=0>
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