x-logic-strategy — Discussions about X-Logic project strategy.

[X-logic-strategy] [X-Logic] X-Logic resurgent

[Roger B. J. <rb...@rb...>]

This first post to the X-Logic blog inaugurates a new phase
in X-Logic, so I will briefly say where it has been and where
I hope it is going.
.
My first start on X-Logic was in January 2000, as an open
source project hosted at SourceForge.net.
That year was not a good one for me and things ground to a
halt in the summer before I had even got off the ground.
At that time I was keen to get something done, so I was
hacking around with XML technologies and not spending much
time writing up what I was trying to do.
The most important thing, I think in retrospect, which I did
then was come up with some small formal models for some
aspects of the X-Logic idea, and these models have kept the
idea alive for me since then even though I haven't
progressed them (other than in my head).
.
I did also produce a small collection of scripts of various
kinds which made it possible to transit my web writing to
XML and made it possible to convert ProofPower formal
specifications and proofs into web pages. These things I
still use, though my formal work is done in LaTeX->PDF these
days.
.
The general conception was then easiest described as some
modern pluralistic distributed approach to Leibniz's lingua
characteristica and calculus ratiocinator. (which I also
think of in my mind as what the QED project should have been
trying to do).
.
Since then, though I kept the idea alive, it has scarcely
moved forward. I have moved forward myself, and one of the
ways I have moved forward is: more exclusively into
philosophy. So whereas I then thought of myself as having a
wide range of interests, including philosophy, I now have
pretty much the same range of interests but consider them
all to be philosophy, so my expectations about what to do
about those interests have shifted. Notably away even from
the possibility of prototyping software. But not away from
high level (architectural) design. Which, when we are
talking about cognitive systems, I think of as "Philosophy
as Engineering".
.
Now, truth be told, even back in 2000 it was these top level
ideas I was interested in working with. But then I didn't
have confidence in the merits of doing design which might
never be implemented. Having spent so much longer, since
then, trying to do philosophy, that doesn't sound so futile
to me now.
.
January 2010 and I am rejigging my philosophical
aspirations, slowly getting a firmer grip on what kind of
philosophical project I might be able to deliver on.
The upshot is "The HOT philosophy project", (for more
details of which see the Roger Bishop Jones blog or
RBJones.com).
This is a book in three parts, the third is "X-Logic", and
alongside this is to be a formal modelling project also
called X-Logic. This one more tightly focussed than the
original X-Logic project and hosted at Google code.
So there is to be one third of a book giving the fullest
story which can be given in English prose, and as much space
as I like for the formal development of a theory about: a
way of organising heterogeneous propositional knowledge
which supports fine discrimination in what we know about the
propositions in question.
.
There is a response to scepticism here, a response to the
idea that one never really knows. And the response is an
elaboration of the pyrrhonean "appearances appear" and the
positivists insistence on science not going beyond the
evidence. The presumption is that, rather than merely
storing what we suppose to be true, we store information
about the grounds we have for believing in the truth.
.
This permits us to reason with uncertain premises (which is
all we ever have) and say something reasonably definite about
the strength of our grounds for belief in the conclusions.
.
I won't go further right now, except to say that I now have
these two principle tracks to get moving.
.
The first is the philosophical, and will begin with an
account of the various considerations which influence my
present conception of X-Logic. This is to be the third part
of the HOT philosophy book. The second is the formal
modelling. I could make a start on this before clarification
at least to the extent of putting together a suitable formal
environment to do the kind of modelling I envisage, and
checking this out by re-doing the models I already have, in
that environment.
.
I would guess that here on the X-Logic blog I will post a
skeleton of the philosophical account which will go in the
book. For more detail, the drafts in PDF and HTML will be
available at RBJones.com
.
I'm not expecting much feedback for a long time, but it
would be welcome.
.
RBJ

--
Posted By Roger Bishop Jones to X-Logic on 3/03/2010 01:46:00 PM

[X-logic-strategy] XML foundation vocabularies (was strategy update note)

[Roger B. J. <rb...@rb...>]

Neil observed (inter alia):

> The idea that meaning of an expression could be defined as
> the expression consequences of the initial expression is an
> idea by one of the philosophers of language (whom, I do not
> remember).

What will do for a philosopher of language may fall short
of an adequate position for a software engineer!

> The idea is simply that we may ask someone what
> they mean by an expression and their expression response
> would be the meaning of the initial expression.

(which is a bit stronger than talking about consequences)
To give an expression when defining or explaining the meaning of
some other expression does not mean that the meaning
_is_ an expression.
It usually means that the meaning of the defined expression is
the same as that of the defined or explained expression.
...
> We might think of this as _formalist_
> meaning. Meaning as the relations strings (expressions) have
> in a particular generating/computable sequence.

> Logic for, say, _formalist_ meaning would be similar to the
> Intuitionist's logic for Constructive mathematics.  An implication
> is a construction/computation and arguments of implication
> states or arguments of the computable function.  There is a
> sense in which the Intuitionist's formalism is an abstraction of
> arbitrary computation.

I associate a formalist conception of meaning with a context
in which the logic is established first and plays a role in axiomatic
definition of the meaning of concepts.

i.e. I associate it with Hilbert's idea that mathematical concepts
should be defined by axiomatisation, which these days one thinks
of usually in the context of first order logic (in which case, however
we know that the meaning of many concepts cannot be completely
caputured by recursive axiom systems).

In my conception of semantics in X-Logic, the semantics of some
XML vocabulary is defined using some other XML vocabulary.
Ultimately this must come to an end!
Let us call an XML vocabulary which is suitable for defining the
semantics of other XML vocabularies but is not itself so defined
(except maybe in terms of itself) a XML foundation vocabulary.

I advocate that an XML foundation vocabulary be defined in
several ways.
(1) in terms of itself
(2) formally (but incompletely)
(3) informally (perhaps by describing how
the formal account is incomplete)

As far as (3) goes this comes down to something quite simple.
e.g. referring to "standard models" of HOL.
(some people will never understand this... you have to accept that
I think)

More specifically I advocate (and may eventually get round to)
obtaining an XML foundation vocabulary by the following means:
(1) define (as above) a simple vocabulary corresponding to HOL
      (polymorphic version of Church's STT)
(2) implement a feature in a HOL proof tool which will export
     theories as definitions of XML vocabularies in terms of the
     vocabulary in context.
(3) apply this to the Galactic Set Theory developed on the X-Logic
     site to export an XML vocabulary for a rich polymorphic higher
     order set theory.

Does any of that make any sense?

Roger
RB...@RB...

Re: [X-logic-strategy] Strategy update note

[Neil N. <n_n...@pa...>]

Roger,

> > The
> > _meaning_ of an expression may be seen as the conse-
> > quence set in the context/theory of that expression.  This
> > then suggests that there may be some fundamental logic
> > application that could be applied to expressions for the
> > purpose of determining meaning.
>
> You can't really establish the meaning of an expression
> until the semantics is defined of the language to which the
> expression belongs.
> The semantics is essentially a prescription of how to
> determine the meaning of any expression.
> In principle one doesn't need a logic thus far, but
> in practice a logic is very handy in defining semantics,
> and in deriving specific conclusions from such a definition.

The idea that meaning of an expression could be defined as
the expression consequences of the initial expression is an
idea by one of the philosophers of language (whom, I do not
remember).  The idea is simply that we may ask someone what
they mean by an expression and their expression response
would be the meaning of the initial expression.  This does not
address what expressions ultimately mean beyond expressions,
but if one was able to uniquely identify the expression
consequences, then for the purpose of expressions--a
bounding condition not necessarily more restrictive than that
usually considered in this area of logic, language, or
mathematics--`meaning' becomes defined in a way that allows
fairly direct analysis.  We might think of this as _formalist_
meaning. Meaning as the relations strings (expressions) have
in a particular generating/computable sequence.

Logic for, say, _formalist_ meaning would be similar to the
Intuitionist's logic for Constructive mathematics.  An implication
is a construction/computation and arguments of implication
states or arguments of the computable function.  There is a
sense in which the Intuitionist's formalism is an abstraction of
arbitrary computation.

> There are indeed interesting connection with your audio work
>
> I previously mentioned that I felt that natural languages
> are best dealt with, so far as logic is concerned, by being
> first translated into a more formal language (even if only behind
> the scenes).
> The audio think is yet one more layer removed, so one
> might then have three layers as follows:
>
> AUDIO LAYER
> == speech recognition ===
> SYMBOLIC NATURAL LANGUAGE
> == formalisation =======
> FORMAL LANGUAGE
>
> A problem well known to AI workers is that these
> translations require a lot of knowledge, so you have to
> go top to bottom and more to disambiguate all sounds.

Yes, the intended audio utility should meet any audio
layer requirement for speech recognition.  At the moment
I estimate the time ratio on my still fairly fast machine will
be in excess of 100 to 1--100 seconds to process 1
second of monophonic sound.  But on the positive side,
the result will identify a worst-case complete solution.
I.e., it will only get better with more analysis and faster
equipment.  But even a high ratio initially can be used
in many applications in audio recording where lead times
for sound in, say, popular music and film may be from
weeks to a year or more.  A Beowulf cluster of about a
dozen of next year's PCs (P4), which would not be out-
of-hand for professional recording studio equipment and
considering that just about all other audio processing
equipment could be replaced, would quickly minimize the
time ratio problem.

I expect that the audio layer for current speech recognition
software is optimized for particular audio functions and
such that current machine capability restrictions trade off
the precision of the audio layer for precision of output.
When the complete solution is obtained it could be relaxed/
optimized for less precision toward a sufficient commercial
speed for speech recognition.

But going from natural language to symbolic natural language
and then to a formal language will have a strong demand
without speech recognition and is an interesting area.

> I am likely to progress more slowly on X-Logic in
> the near future since I have a new contract starting
> up which will take priority.

This is very good to hear.

I have beat the frequency crosstalk problem and am
now working on combining these finely divided vertical
frequency spectrums (spectrum slices) into individual,
horizontal frequency and amplitude functions.  Each
frequency's duration definition in a song (roughly a note)
might be seen as a different colored stand of spaghetti,
and at the moment all those different colored strands
have been finely diced and I need to collect those small
pieces of each strand back together into a whole strand.

Regards,

Neil Nelson

Re: [X-logic-strategy] Strategy update note

[Roger B. J. <rb...@rb...>]

Neil,

Thanks for your message.

 > As you can see I can go on at length about this but I
> also think your project is important in that I would say
> information generally has a logic description.

As I would put it, any language with a well-defined semantics
can be given a logic.

> The
> _meaning_ of an expression may be seen as the conse-
> quence set in the context/theory of that expression.  This
> then suggests that there may be some fundamental logic
> application that could be applied to expressions for the
> purpose of determining meaning.

You can't really establish the meaning of an expression
until the semantics is defined of the language to which the
expression belongs.
The semantics is essentially a prescription of how to
determine the meaning of any expression.
In principle one doesn't need a logic thus far, but
in practice a logic is very handy in defining semantics,
and in deriving specific conclusions from such a definition.

> And then because there
> is a large and growing volume of computer based
> expression, there could be significant and widespread
> use of such an application.

I am certainly intending  a framework which extends to
all notations in well-defined languages.

> My ideal logic
> application, would be much like an extension of common
> web search engines that would identify, assemble, and
> condense web material according to my objectives that may
> be given in a back and forth manner (perhaps very detailed)
> as we are doing here.  Also I would want it to project or
> prototype solutions.  It would gather information and solve
> problems or be a key component of such an application.

This pretty much corresponds to the X-Logic query engine.
One would expect to begin with rather more limited capabilities.

There are indeed interesting connection with your audio work 

I previously mentioned that I felt that natural languages
are best dealt with, so far as logic is concerned, by being
first translated into a more formal language (even if only behind
the scenes).
The audio think is yet one more layer removed, so one
might then have three layers as follows:

AUDIO LAYER
== speech recognition ===
SYMBOLIC NATURAL LANGUAGE
== formalisation =======
FORMAL LANGUAGE

A problem well known to AI workers is that these
translations require a lot of knowledge, so you have to
go top to bottom and more to disambiguate all sounds.

This may or may not have any connection with your
work.

I am likely to progress more slowly on X-Logic in
the near future since I have a new contract starting
up which will take priority.

I have set up a new project "MaD-portal" for the portal
work and will use this for the web site software initially
started under X-Logic, apart from the X-Logic specifics.
I am evaluating the hosting facilities at sourceforge to see
if they are up to the job.
I think we need php+mysql+xml and incoming mail processing.
So far, though I am supposed to have a database I can't get at it.

regards,
Roger
RB...@RB...

Re: [X-logic-strategy] Strategy update note

[Neil N. <n_n...@pa...>]

Roger,

Please excuse me for not getting back to you earlier.  I
have been doing work on one of my primary projects that
is the complete Fourier reduction of common music or
natural sounds.  The purpose is to translate audio to a
Fourier description upon which operations may be
performed and then back to the audio.  Though there
may be standard approaches for doing this, there do not
appear to be any easily available that are sufficiently
precise to, say, reverse the combined waveform of an
arbitrary small collection of frequencies (usually not
unit frequencies) back to the Fourier description from
which the waveform has been generated within an error
difference below a reasonable level of audio detection,
i.e., to a point indiscernible by the ear.

This is not a project of relevance to X-logic, but is, I
believe, a very fundamental project in the human-
computer audio interface such that if the objective could
be achieved, there would be significant and widespread
applications.  What we hear is more immediately to us a
Fourier description (translation) such that we can see the
single waveform audio signal as an encoding of that
description.  And then the raw description would be
analyzed for structure similarities (pattern recognition) that
may become text in speech recognition or the sound of a
flute as against that of a violin; we hear/recognize sound
sources and certain kinds of information.

The task is one of noise reduction: beyond the basic
Fourier analysis, as that basic analysis still exhibits a
significant amount of noise and a description much larger
than started with, what are those frequency, amplitude,
and phase functions that will push the noise (primarily)
and the description lower?

As you can see I can go on at length about this but I
also think your project is important in that I would say
information generally has a logic description.  The
_meaning_ of an expression may be seen as the conse-
quence set in the context/theory of that expression.  This
then suggests that there may be some fundamental logic
application that could be applied to expressions for the
purpose of determining meaning.  And then because there
is a large and growing volume of computer based
expression, there could be significant and widespread
use of such an application.

My project is to identify a utility that is the maximal human
hearing information interface, whereas I think of your project
as the utility for representing expression meaning.  Once I
get my application to a useable condition, I could then go
to the large number of audio-related industries in my area--
I live in the middle of one of the largest (if not the largest)
concentrations of such industries in the world--and show
them the significant increase in audio control and processing
capabilities provided by my application.  My ideal logic
application, would be much like an extension of common
web search engines that would identify, assemble, and
condense web material according to my objectives that may
be given in a back and forth manner (perhaps very detailed)
as we are doing here.  Also I would want it to project or
prototype solutions.  It would gather information and solve
problems or be a key component of such an application.

But anyway, I need to begin analysis on a kind of cross-
talk distortion frequencies have on each other as seen in the
Fourier analysis: How is the distortion reduced for two
arbitrary frequencies, and then three, and so on?  And then
as it seems that this class of question is essentially a search
for an optimal function in a moderately bounded space I
should be able to identify a general search procedure in
which my current programs can be embedded.

But I am interested in your project and look forward to
your consideration of the focussed application.

Sincerely,

Neil Nelson


> Here's a brief note on my present view of the X-Logic
> development strategy.
>
> X-Logic needs I believe to be focussed on an application
> which can deliver worthwhile functionality early.
> Then the higher level stuff can be driven by that application,
> bottom up.
>
> I propose that this should be an X-Logic query engine
> implementing a useful fragment of a an X-Logic query
> language, for use in the MaD portal.
>
> The X-Logic query engine would eventually be a separate
> project in its own right, but not for some time yet.
>
> The present work on the web site will have to be transferred
> out of X-Logic, because it is based on GPL code and
> cannot therefore be issued as part of the X-Logic project,
> which is not GPL.
>
> I shall start off the MaD portal as a sourceforge project
> from the existing hacked phpnuke.
> Then the X-Logic site can be changed to use the MaD
> website as a comment/forum server.

[X-logic-strategy] Strategy update note

[Roger B. J. <rb...@rb...>]

Here's a brief note on my present view of the X-Logic
development strategy.

X-Logic needs I believe to be focussed on an application
which can deliver worthwhile functionality early.
Then the higher level stuff can be driven by that application,
bottom up.

I propose that this should be an X-Logic query engine
implementing a useful fragment of a an X-Logic query
language, for use in the MaD portal.

The X-Logic query engine would eventually be a seperate
project in its own right, but not for some time yet.

The present work on the web site will have to be transferred
out of X-Logic, because it is based on GPL code and
cannot therefore be issued as part of the X-Logic project,
which is not GPL.

I shall start off the MaD portal as a sourceforge project
from the existing hacked phpnuke.
Then the X-Logic site can be changed to use the MaD
website as a comment/forum server.

Roger Jones
RB...@RB...