symbolic equation?

[Paola Di Maio]

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  

[Paola Di Maio]

I am not a mathematician, but I love to browse the encyclopedia of mathematics

I found some references in Matlab and recent papers but there is no such thing (that I could find) in the Encyclopedia of Mathematics

https://encyclopediaofmath.org/index.php?title=Special%3ASearch&search=%22symbolic+equation%22&button= 

 

[Ravi Sharma]

Paula

Unless all symbols are defined, it is not easy for me to understand t that equation.

Also the comment that it would explain Dark matter is far far from likely.

Why did you choose that equation? Was anything in particular.

Yes Janet and George and John are explaining somethings about Symbolic models and relationships to Knowledge Graphs, stay tuned in talks and communique related tracks pages 

Thanks

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Thanks.
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(Dr. Ravi Sharma)

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[Paola Di Maio]

Ravi

thanks

The slide was liked by Lecun in social media yesterday, but it did not seem to match any defintion nor description of symbolic AI

in use  It is obvious that the ML community does not understand symbolic KR

I shared  my notes on symbolic knowledge representation and symbolic integration with  a couple of people on this list this year, but received no feedback btw

I now hear that the topic is picking up?

I therefore wanted to check if someone could advise, according to the encyclopedia, is this  another sign of absolute madness coming from ML?

PDM

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[Alex Shkotin]

Paola,

The leader of symbolic computing is Stephen Wolfram with his greate project https://www.wolframalpha.com/ and his last insight is that our world is just a dynamic graph with 10^400 nodes or edges.

Finally We May Have a Path to the Fundamental Theory of Physics… and It's Beautiful—Stephen Wolfram Writings 

Enjoy,

Alex 

сб, 27 июн. 2020 г. в 10:13, Paola Di Maio <paola....@gmail.com>:

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[Paola Di Maio]

Thanks 

I obviously think this work is great but never linked it to symbolism as such

Maybe he could give us a talk to make that more explicit?

PDM

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[Alex Shkotin]

Paola,

We discussed here in group the achievement of ANN people: they trained ANN to integrate symbolically math expressions of suitable kind - it's quicker than algorithms but not every time correct. And they check correctness by differentiating the rezult:-)

Alex

сб, 27 июн. 2020 г. в 10:13, Paola Di Maio <paola....@gmail.com>:

Ravi

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[Alex Shkotin]

Paola,

Are you asking specifically about this particular symbolic equation?

Alex

сб, 27 июн. 2020 г. в 02:41, Paola Di Maio <paola....@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  

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[Paola Di Maio]

yes, I could not find any reference in the history of maths to symbolic equations

as constructs

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[Alex Shkotin]

Well, usually they just do not add "symbolic" as a) any usual equation is symbolic, and b) the question "what does it mean non-symbolic equation?" arise.

But from context it's more or less clear that the "symbolic equation" there is just the usual math equation.

like this "We find the correct known equations, including force laws and Hamiltonians, can be extracted from the neural network. We then apply our method to a non-trivial cosmology example-a detailed dark matter simulation-and discover a new analytic formula which can predict the concentration of dark matter from the mass distribution of nearby cosmic structures."

сб, 27 июн. 2020 г. в 12:05, Paola Di Maio <paola....@gmail.com>:

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[Alex Shkotin]

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....@gmail.com>:

yes, I could not find any reference in the history of maths to symbolic equations

as constructs

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[James Davenport]

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

 

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

 

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[Paola Di Maio]

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  

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[Alex Shkotin]

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....@gmail.com>:

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[Paola Di Maio]

Yes I think I am seeing that

Please share exciting examples

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[John F. Sowa]

Alex, Paola, Ravi, James, List

I'll just make a few comments on some of the issues.

Re notation:  Mathematicians don't think in words.  They think in two ways that are far more  fundamental than words:  (1) images about the subject matter (geometry, for example); and (2) mathematical notations, which are more universal than the words used to describe them in any language around the word.

For a simple example, when you're doing arithmetic, with a calculator or with pencil and paper, do you think of or even remember how you were taught?   Does anybody think about the words 'minuend' and 'subtrahend' when doing subtraction?  

Mathematicians never think about the way any teacher defined the word 'equation'.  They just write the symbol '=' and use it in their theorems, proofs, and computations.  The words are totally irrelevant because they're totally forgotten.

Re Wolfram:  His company developed Mathematica,  a collection of excellent tools for helping professional scientists, engineers, and mathematicians do complex symbolic computations.  There are also free tools, such as Mathlab, which are also widely used. People around the world use these tools without thinking about the words their teachers used in some long-forgotten classroom.

Re what is fundamental:  For professionals in any field, the level that is fundamental  is the level they use in talking with their colleagues, students, teachers, customers, managers, funding agencies, etc.  This point is true for any profession from farming and cooking to astronomy and brain surgery.  The word 'fundamental' is relative to the subject matter.

Re neuroscience:  In ancient times (1990s, for example) people like Paul and Patricia Churchland used the term 'folk psychology' to deprecate the way people talk about their thinking, feeling, and emotions.  They claimed that someday in the future, people would learn to use more precise neural terminology instead of  talking about their feelings.

But today, the neuroscientists have far more respect for the way people talk about their feelings than they have for the Churchlands.  In experiments with fMRI scanners, for example, the words that people use to describe their thoughts and feelings are the raw data, which the scientists correlate with what they brain scans show.  The words that ordinary people use to describe their feelings are essential data.  The scientists  don't call it "folk psychology".

For examples, see the slides in Section 6 of http://jfsowa.com/talks/eswc.pdf .

For even more examples, see the slides for "The virtual reality of the mind": http://jfsowa.com/talks/vrmind.pdf .  (I extracted some of these slides for Section 6 of eswc.pdf.)

John

[James Davenport]

I agree with John inasmuch as he is describing thinking. But surely ontologies are for storing and communicating, and here it does matter (as that paper points out). I recall a Masters-level lecture of mine in France falling flat because they do grade-school division differently.

     James

 

From: ontolo...@googlegroups.com <ontolo...@googlegroups.com> On Behalf Of John F. Sowa
Sent: 27 June 2020 15:15
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Subject: Re: [ontolog-forum] Re: symbolic equation?

 

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Alex, Paola, Ravi, James, List

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[John F. Sowa]

James,

Yes.  That is a concern:

JD> I agree with John inasmuch as he is describing thinking. But surely ontologies are for storing and communicating, and here it does matter (as that paper points out). I recall a Masters-level lecture of mine in France falling flat because they do grade-school division differently.

Solution:  Make the formal definitions *normative*.  Then translate those definitions to a version of English that is described as *informative*.   If there is any doubt about the English version, state that the formal version takes priority.

If you want a source of definitions for mathematical terms, see Mathematica or Mathlab.  Since Mathematica is proprietary, Mathlab is probably a better source for the definitions.  But it would be a good idea to check any definitions with Mathematica to make sure that there aren't any discrepancies.

John

[James Davenport]

Or indeed OpenMath.

James Davenport

Hebron & Medlock Professor of Information Technology, University of Bath
National Teaching Fellow 2014;  DSc (honoris causa) UVT
OpenMath Content Dictionary Editor
Former Fulbright CyberSecurity Scholar (at New York University)
Former Vice-President and Academy Chair, British Computer Society

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James,

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[Alex Shkotin]

I will. Sorry can't find this integration-differentiation paper.

сб, 27 июн. 2020 г. в 15:23, Paola Di Maio <paola....@gmail.com>:

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[Alex Shkotin]

I got it https://groups.google.com/d/msg/ontolog-forum/MuVb2mRSACc/E2oX4krcAAAJ

сб, 27 июн. 2020 г. в 15:23, Paola Di Maio <paola....@gmail.com>:

Yes I think I am seeing that

Please share exciting examples

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[John F. Sowa]

Paola,

Every ANN that has ever been designed and used maps symbols to symbols. For examples, please look at slide 36 of http://jfsowa.com/talks/eswc.pdf .

The table at the top of the slide is by Andrew Ng, who is an  expert in designing and developing ANNs.  The comments about that table are summaries of what Ng said in the video, which I cited at the bottom of that slide.

PDM> 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.

For pattern recognition, the input for a typical  ANN is a matrix of symbols (triads of numbers for Red, Green, and Blue) that represent the colors of pixels in a photograph.  The output is a symbol (or structure of symbols) that describes the image represented by those pixels.

In the Alpha Go system, which beat the world champion at Go, the ANN for the evaluation function mapped symbols that represented stones on a Go board to symbols (numbers) that estimated the strength of a particular Go position for one player or the other.

Although the Alpha  Go designers gave most of the credit to the ANN, the system was actually a hybrid.  It used many symbolic steps to play the game and search different options.  There was only one step that used an ANN:  evaluate a board position to estimate which player had a better position.

Research issue:   Instead of using one or more ANNs to do all the steps of cognition, find some way of subdividing the task into a variety of different kinds of tasks that must be performed.   Then determine which of those tasks could be handled better by an ANN or by some symbolic method.

John

[Paola Di Maio]

Hello John, thank you

Thank you for the slides-  to say cat is on the mat other than language I like existential and conceptual graphs the best, they are the most computatioanally efficient!

I think when we use the word symbolic we may have start disambiguating, at which level.

Of course, computational symbols are alphanumeric. (this is what Ng referes to I think)

  Are pictures that do not contain alphanumeric characters symbolic? I think so (a picture of an umbrella or a house is highly symbolic from a semiotic point of view

is musical notation symbolic, I think so

  Are audio signals, sounds, also symbols?  more directly related to perception 

For more understanding of symbols, we study signs, semiotic, etc

But here I was referring to the expression symbolic equation does not seem to make sense as a symbolic knowledge representation 

The use of alphanumeric symbols had nothing to do with symbolic AI, whereby symbolic AI adopts symbolic KR, as we learn also from your book. 

But in ML papers now people are mixing the two levels-  and in addition to various computational headaches including p-values and general understandability and reproducibility fo the algorithms, now we have to be careful to see what exactly are they doing and saying when they say symbolic?  Symbolic KR can be used to explain that-

The sentence you attribute to me below actually Alex's r. no worries

PDM>ALEX 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.  

PDM

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[Paola Di Maio]

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

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[Michael Denny]

When you diagram a sentence you get a tree so I suppose as long as an equation can be expressed in a sentence it also resides as a tree.

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[Paola Di Maio]

Thank you Michael

will make my life so much simpler, but I ll need a lot more space 

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[Paola Di Maio]

Thank you Milton

thats the point I think

the expression is the slide is an equation. 

why say 'symbolic equation'  or symbolic expression and mess things up?

this is what I mean by mixing indiscriminately terminology concepts from maths, computation, AI and ML indiscriminately is contributing to the inextricable mess and increasing the challenge to understandability 

I know, there may be not a complete encyclopedia of maths, but I cannot possibly read all the literature in the world to find out if something people mention exists (in scholarly terms) or not, and if it exists, what does it refer to really?

So I use encyclopedias as a kind of ontology for the maths domain

Let me know if you have a better way of finding out if any pseudo mathematical concept being leveraged in ML exist or nor

@all;

where do mathematical matlab (John I think you mean matlab not mathlab? I also get it wrong) and openmath get their facts from?

On Sun, Jun 28, 2020 at 8:00 AM ProjectParadigm-ICT-Program <metadat...@yahoo.com> wrote:

What are you referring to?  It seems the expression used "symbolic equation" should be mathematical equation.

And for the record there is no complete encyclopedia of modern mathematics.

The image in the tweet is a pipe dream. To get from the graph network to the mathematical equation is utter simplification. Science requires that a hypothesis must be falsifiable. Running the same data with multiple AI systems will still require humans to validate the hypothesis. Testing the hypothesis requires a level of reasoning that can produce e.g. though experiments or comparison with similar theories in other fields. And also requires an interplay of formal and non-formal thinking and switching between natural language and mathematical expression that is beyond the current grasp of AI.

Milton Ponson
GSM: +297 747 8280
PO Box 1154, Oranjestad
Aruba, Dutch Caribbean
Project Paradigm: Bringing the ICT tools for sustainable development to all stakeholders worldwide through collaborative research on applied mathematics, advanced modeling, software and standards development

[Alex Shkotin]

John,

Your "Re Wolfram:  His company developed Mathematica,  a collection of excellent tools for helping professional scientists, engineers, and mathematicians do complex symbolic computations." is like thinking of Google just mentioning only its search engine i.e. first successful project.

Please look at his bio (projects part). For me we should compare https://www.wolframalpha.com/ QAS with successful Cyc:-)

This QAS does not know "symbolic equation" but does "ontology".

Alex

сб, 27 июн. 2020 г. в 17:15, John F. Sowa <so...@bestweb.net>:

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[James Davenport]

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

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[Paola Di Maio]

James

that good to know thanks, I wonder

could you or your system help to translate algebra instructions for origami making into

trees?

here some models

https://oriwiki.com/  

here our project

https://github.com/Starborn/Origami/wiki/Origami-Rationale,-Outline  

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[James Davenport]

Good question.  But OpenMath is purely an ontology, not a system.

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