Hi,

such a tool could be interesting. However, we are lacking concrete
examples on PRESS abilities. It would be nice if you could provide some
examples (and perhaps benchmarks), especially for things that Sage's solve
command is not able deal with correctely (they are tons, just have a look
on https://ask.sagemath.org). The only example i could find in the
testing/ directory on the public reposiroty, is log(x,2) + 4*log(2,x) == 5
(in Sage's notations), which does not tell much about PRESS abilities.

Ciao,
Thierry


On Wed, Oct 12, 2016 at 02:25:20AM -0400, Ted Kosan wrote:
> William wrote:
> 
> > The term "AI", especially in the 1990s, has a bad reputation among
> > some people, due to having massively over-promised and
> > under-delivered.  It  got hyped like crazy by both academics and
> > companies at certain points in the past.    The term can -- in some
> > cases -- cause some people who have been paying attention to CS
> > research for a few decades (such as RJF) to cringe.
> >
> > For what it is worth, in recent years, there is a field that's been
> > labeled "machine learning", (which is of course closely related to
> > statistics, AI, etc.).  The term "machine learning" is generally
> > viewed in a fairly positive light, since the practioners tends to make
> > more limited claims, and have had some impressive recent successes
> > (e.g., beating top human Go players, doing automatic language
> > translation, etc.).
> 
> A very useful thing to know about the neural net type of machine
> learning that has been enjoying success recently (due to deep learning
> techniques) is there was a time around 2004 when even the top
> researchers in the area such as Hinton and LeCun couldn't even get
> their papers published because the broader machine learning community
> thought neural net AI had been proven to be a failure. It wasn't until
> deep learning researchers completely destroyed non-deep learning
> competitors in the ILSVRC computer vision competition in 2012 that
> these doubters were proven wrong.
> 
> Just as the majority of people were wrong about neural net-based AI
> being ineffective, the majority of people are currently wrong about
> logic-based AI being ineffective. PRESS is an excellent example
> because it was one of the top AI programs that was developed during
> the 1970s and 1980s, and it works very well. There are a number of
> effective logic-based AI programs that have been developed since the
> 1970s which, like PRESS, have been mostly forgotten or ignored.
> 
> The machine learning type of AI is indeed currently meeting with great
> success. However, most of this type of AI is of limited use in
> education because it is unable to explain how it arrives at the
> answers it provides. As Doug Lenat says, machine learning AIs can be
> thought of as "idiot savants" that have no understanding of the areas
> they are designed to work in. Logic-based AIs will become the dominant
> kind of AIs in the future because this kind of AI does understand its
> subject matter.
> 
> 
> 
> > My position: Ted, whatever you want to call it, many thanks for
> > sharing your work with us Sage devs.  It is really potentially very
> > valuable to possibly massively enlarge the range of people who might
> > use Sage.  We sage devs have done relatively little in quite some time
> > to enlarge the potential user base of Sage itself.
> 
> If a step-by-step equations solver that is based on PRESS does become
> part of Sage, I think it is important to advertise the fact that some
> of the most effective AI technology ever developed has been added to
> Sage, and that it has the potential to teach many areas of mathematics
> much more effectively than human teachers are capable of doing.
> 
> Ted
> 
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