Has anyone made equations out of English sentences?

[Scott Jensen]

I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.

It might look something like:

"The raven is a black bird."

"raven = black + bird"

The idea being that you could take a document, use the rules to translate
the English sentences into math equations, and distill it down into its
informational parts and total them for what the document equaled in
information.

So far my net search for this has turned up nothing. I am hoping it is
simply because I'm not using the proper termnology when doing my search. If
you can tell me the proper termnology for this sort of thing, that would be
of great help. Or, better yet, if you could give URLs to where this stuff
is located, that would be fantastic!

Thanks in advance!

Scott Jensen

[John Ramsay]

Of course it's been done. Have you never heard
of computer languages?

They convert language into a mathematical code.

You would not have been able to
post your message without them.

Post by Scott Jensen
I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.
"The raven is a black bird."
"raven = black + bird"
The idea being that you could take a document, use the rules to translate
the English sentences into math equations, and distill it down into its
informational parts and total them for what the document equaled in
information.
So far my net search for this has turned up nothing. I am hoping it is
simply because I'm not using the proper termnology when doing my search. If
you can tell me the proper termnology for this sort of thing, that would be
of great help. Or, better yet, if you could give URLs to where this stuff
is located, that would be fantastic!
Thanks in advance!
Scott Jensen

[ray o'hara]

Post by John Ramsay
Of course it's been done. Have you never heard
of computer languages?
They convert language into a mathematical code.
You would not have been able to
post your message without them.

Post by Scott Jensen
I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.
"The raven is a black bird."
"raven = black + bird"
The idea being that you could take a document, use the rules to translate
the English sentences into math equations, and distill it down into its
informational parts and total them for what the document equaled in
information.
So far my net search for this has turned up nothing. I am hoping it is
simply because I'm not using the proper termnology when doing my search.

If

Post by John Ramsay

Post by Scott Jensen
you can tell me the proper termnology for this sort of thing, that would be
of great help. Or, better yet, if you could give URLs to where this stuff
is located, that would be fantastic!
Thanks in advance!
Scott Jensen

That's not what he meant.


P.S. this isn't Jeopardy, the reply goes after the question. Top posting
disruptes the natural flow of the conversation.

[ray o'hara]

Post by Scott Jensen
I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.
"The raven is a black bird."
"raven = black + bird"

black + bird need not equal raven. crows starlings,cowbirds, grackles not to
mention several others are all black birds. A language that could be so
reduced would be inadequate to the needs of communication.

[Scott Jensen]

Post by ray o'hara

Post by Scott Jensen
I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.
"The raven is a black bird."
"raven = black + bird"

black + bird need not equal raven. crows starlings,cowbirds, grackles not to
mention several others are all black birds. A language that could be so
reduced would be inadequate to the needs of communication.

First, I gave the above as an example.

Second, it was meant to illustrate how the sentence could be translated.
Yes, I know other birds are also black, but that's not what the sentence
provided as information.

Scott Jensen

[Titian]

Post by Scott Jensen

Post by ray o'hara

Post by Scott Jensen
I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.
"The raven is a black bird."
"raven = black + bird"

black + bird need not equal raven. crows starlings,cowbirds, grackles not to
mention several others are all black birds. A language that could be so
reduced would be inadequate to the needs of communication.

First, I gave the above as an example.
Second, it was meant to illustrate how the sentence could be translated.
Yes, I know other birds are also black, but that's not what the sentence
provided as information.
Scott Jensen

Scott

look for a book called "The Maths Gene" by Keith Devlin which I believe
approaches this idea from another direction....mathematical ability is
related to the human brain inventing language (I think!)

Titian

[Scott Jensen]

Post by Titian
look for a book called "The Maths Gene" by Keith Devlin
which I believe approaches this idea from another direction
....mathematical ability is related to the human brain inventing
language (I think!)

Thanks. I've requested it through my local public library.

Scott Jensen

[ray o'hara]

Post by Scott Jensen

Post by ray o'hara

Post by Scott Jensen
I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.
"The raven is a black bird."
"raven = black + bird"

black + bird need not equal raven. crows starlings,cowbirds, grackles

not

Post by Scott Jensen

Post by ray o'hara
to
mention several others are all black birds. A language that could be so
reduced would be inadequate to the needs of communication.

First, I gave the above as an example.
Second, it was meant to illustrate how the sentence could be translated.
Yes, I know other birds are also black, but that's not what the sentence
provided as information.
Scott Jensen

I was showing how a simple sentence like that had too many variables.

[Scott Jensen]

Post by ray o'hara

Post by Scott Jensen

Post by ray o'hara

Post by Scott Jensen
I am interested to know if anyone has developed mathematical
translation rules that takes English sentences and converts them
into equations that produce a sum. Or if someone has done it
for another language and an English version of the rules has
been done.
"The raven is a black bird."
"raven = black + bird"

black + bird need not equal raven. crows starlings,cowbirds,
grackles not to mention several others are all black birds. A
language that could be so reduced would be inadequate to the
needs of communication.

First, I gave the above as an example.
Second, it was meant to illustrate how the sentence could be
translated. Yes, I know other birds are also black, but that's
not what the sentence provided as information.

I was showing how a simple sentence like that had too many
variables.

I think you read more into that than what I was doing. I was showing how
that specific sentence would be converted. You brought in outside
information that the sentence didn't provide and thought your information
then invalidated the equation.

What I am seeking is a lead or ideally a URL to anyone that has attempted
sentence conversion. I am not seeking perfect conversion. Just the
conversion of sentences into mathematical equations.

Scott Jensen

[Stephen Calder]

Post by Scott Jensen
I think you read more into that than what I was doing. I was showing how
that specific sentence would be converted. You brought in outside
information that the sentence didn't provide and thought your information
then invalidated the equation.
What I am seeking is a lead or ideally a URL to anyone that has attempted
sentence conversion. I am not seeking perfect conversion. Just the
conversion of sentences into mathematical equations.

You seek what is nonexistent.

[John Flynn]

Post by Scott Jensen
I think you read more into that than what I was doing. I was showing
how that specific sentence would be converted. You brought in outside
information that the sentence didn't provide and thought your
information then invalidated the equation.

You're going to have to decide, though, how much 'outside information'
to allow, since we don't utter sentences in complete isolation. We
bring a huge amount of background knowledge to every interpretation of
every sentence.

Consider interpreting the sentence:
"Fred ate an ice-cream."

We already have the knowledge that "Fred" is probably a human
being. Probably, but it's not certain. If we met this sentence
out of nowhere, in perfect isolation, we would be best taking "Fred"
to be a human. But if there were preceding context that identified
"Fred" as being a parrot, then that would have to be brought into the
interpretation and included in the 'equation' you're looking for.
It would alter the meaning and maybe even the truth or believability
of the sentence (thus affecting its usable information content).

Now, imagine if you met the following in the same perfectly
isolated context:
"Fred ate my homework."
We would need to know from 'outside information' that "Fred" is
now less likely to be a human. There's nothing in the sentence
construction that changes this likelihood, so we *must* rely on
'outside information'. In fact, very specific 'outside information'
(i.e., the cliché about my dog eating my homework) narrows the
interpretation even further. The informational content of the
sentence now includes some implications that "Fred" is actually a
dog, not just that he ate my homework. The information is there
to be extracted so isn't it a good idea to include it in any
equation suggested to derive the informational content? To do so,
however, means working out some way of accommodating when and where
to use the 'outside information' we bring to the recovery of the
sentence's meaning.

Then, consider these sentences:
"The dog ate my letter."
"The fax machine ate my letter."
To work out what information these are giving us, we would need to
resort to things that are not explicitly stated in the sentences
themselves.

The short answer is that attempts to reduce natural language to neat
and tidy semantic formalisms are immensely difficult unless one is
willing to either:
1. Restrict the available definitions that your words can have
(i.e., so every word can have one meaning and one meaning only)
and/or restrict the type of sentences that you can process in
this system (e.g., only process "X is Y" types).
Or:
2. Accept that there will be a whole heap of manual tweaking to
make sure the intended interpretation is extracted (i.e., bring
in all the unstated implications and presuppositions that we
don't bother mentioning because the context and our own world-
knowledge fill in the gaps).

[Chris Croughton]

On Mon, 8 May 2006 12:30:56 -0500, Scott Jensen

Post by Scott Jensen
I think you read more into that than what I was doing. I was showing how
that specific sentence would be converted. You brought in outside
information that the sentence didn't provide and thought your information
then invalidated the equation.

However, you need that "outside information" in order to parse the
sentence. Consider the canonical ambiguous sentence:

Time flies like an arrow.

There are at least three ways of parsing that:

Simile:

time flies (verb) like (in a similar way) an arrow [flies]

Eating habits:

"time flies" (some sort of insect) like (verb) an arrow [to eat]
(compare "fruit flies like a banana")

Command:

[You] time [those] flies like (in a similar way) an arrow [times
flies]

Which is correct? Only context can determine it, and not always then.

Post by Scott Jensen
What I am seeking is a lead or ideally a URL to anyone that has attempted
sentence conversion. I am not seeking perfect conversion. Just the
conversion of sentences into mathematical equations.

What you are asking for is a general algorithm for parsing natural
language. It doesn't exist, if it did those who created it would be
making a lot of money. But even humans can't unambiguously parse
natural language, as shown above, let alone put it into a
pseudo-mathematical language. Even computer languages like Prolog still
have very rigid syntax compared to natural languages.

Note that the term 'equation' implies equality, as in your "raven =
black + bird", but that isn't the information actually conveyed by the
sentence "a raven is a black bird". The actual information is more
complex, and is more accurately stated in English as "a raven is a type
of bird which is also black". In a pseudo-mathematical form, where =>
is the relationship 'implies':

raven => object(type=bird, colour=black)

A crow would also have the same description, as would a blackbird and
many others (assuming that the colour is the main colour, all of them
also have other colours as well, for instance yellow beaks). It isn't
an equality, not all birds coloured black are ravens.

Chris C

[Don Phillipson]

Post by Scott Jensen

Post by ray o'hara

Post by Scott Jensen
I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.
"The raven is a black bird."
"raven = black + bird"

black + bird need not equal raven. crows starlings,cowbirds, grackles

not

Post by Scott Jensen

Post by ray o'hara
to
mention several others are all black birds. A language that could be so
reduced would be inadequate to the needs of communication.

First, I gave the above as an example.
Second, it was meant to illustrate how the sentence could be translated.
Yes, I know other birds are also black, but that's not what the sentence
provided as information.

This is just the point . . .
"That's not what the sentence provided as information"
is a valid defence in this debate only if we can cite accepted
rules of meaning or logic that would substantiate:
A: "The raven is a black bird."
B: "raven = black + bird"
C: black + bird need not equal raven
Therefore D: proposition C contradicts either A: or B (or both.)

We have no such rules, i.e. neither linguists nor machine translators
nor philosophers have yet found rules of information of such power
as to decide disputes of this type. But we know:
1. Natural languages have evolved and continue to change.
They are nowadays understood better than 50+ years ago, but
we hope our understanding of natural languages will improve
much more.
2. Formal languages can be created and understood in detail
-- but probably incompletely, perhaps never completely (cf. Godel etc.)

[Scott Jensen]

Post by Don Phillipson

Post by Scott Jensen

Post by ray o'hara

Post by Scott Jensen
I am interested to know if anyone has developed
mathematical translation rules that takes English
sentences and converts them into equations that
produce a sum. Or if someone has done it for
another language and an English version of the
rules has been done.
"The raven is a black bird."
"raven = black + bird"

black + bird need not equal raven. crows starlings,
cowbirds, grackles not to mention several others are
all black birds. A language that could be so reduced
would be inadequate to the needs of communication.

First, I gave the above as an example.
Second, it was meant to illustrate how the sentence could
be translated. Yes, I know other birds are also black, but
that's not what the sentence provided as information.

This is just the point . . .
"That's not what the sentence provided as information"
is a valid defence in this debate only if we can cite accepted
A: "The raven is a black bird."
B: "raven = black + bird"
C: black + bird need not equal raven
Therefore D: proposition C contradicts either A: or B (or both.)

Actually, no, it can be "black + bird = raven", if that is all that "black +
bird" totals in the database.

Post by Don Phillipson
We have no such rules, i.e. neither linguists nor machine translators
nor philosophers have yet found rules of information of such power
1. Natural languages have evolved and continue to change.
They are nowadays understood better than 50+ years ago, but
we hope our understanding of natural languages will improve
much more.
2. Formal languages can be created and understood in detail
-- but probably incompletely, perhaps never completely (cf.
Godel etc.)

It is hard for me to imagine that no one has ever attempted what I propose.
I'm not asking for prefection. I don't care if it only works with simple
sentences. Can someone at least point me to a newsgroup, website,
university, or somewhere that might know of such an attempt?

Scott Jensen

[Stephen Calder]

Post by Scott Jensen
I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.
"The raven is a black bird."
"raven = black + bird"
The idea being that you could take a document, use the rules to translate
the English sentences into math equations, and distill it down into its
informational parts and total them for what the document equaled in
information.

I don't believe this is possible at the present level of technology.

It would make machine translation, for example, very simple and it
ain't. Not yet.

Unless you're talking about a simple checksum. That's another story.

[Scott Jensen]

Post by Stephen Calder
Unless you're talking about a simple checksum. That's another
story.

Simple checksum being?

Scott Jensen

[izzy]

Post by Scott Jensen
Simple checksum being?

An algorithmic device, such as a "check digit" that indicates if a
simple transposition or substitution error has occurred in a string of
digits.

Speaking of ravens, the Mad Hatter asked "Why is a raven like a writing
desk".
Izzy's answer is:
The raven has a secret aerie.
A writing desk is a secretary.

ciao,
Israel "izzy" Cohen

[Stephen Calder]

Post by Scott Jensen

Post by Stephen Calder
Unless you're talking about a simple checksum. That's another
story.

Simple checksum being?
Scott Jensen

Sometimes in order to verify that a document has not been altered, the
number of each character in the document is used as part of a sum. Any
alteration in the document changes the checksum.

[Philip Baker]

In article <kIA7g.402$***@fe03.lga>, Scott Jensen <***@charter.net>
writes

Post by Scott Jensen
I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.
"The raven is a black bird."
"raven = black + bird"
The idea being that you could take a document, use the rules to translate
the English sentences into math equations, and distill it down into its
informational parts and total them for what the document equaled in
information.
So far my net search for this has turned up nothing. I am hoping it is
simply because I'm not using the proper termnology when doing my search. If
you can tell me the proper termnology for this sort of thing, that would be
of great help. Or, better yet, if you could give URLs to where this stuff
is located, that would be fantastic!

You might want to take a look at the Prolog programming language.

[Scott Jensen]

Post by Philip Baker
You might want to take a look at the Prolog programming
language.

Thanks. I will.

Scott Jensen

[j***@yahoo.com]

Post by Scott Jensen
I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.
"The raven is a black bird."
"raven = black + bird"
The idea being that you could take a document, use the rules to translate
the English sentences into math equations, and distill it down into its
informational parts and total them for what the document equaled in
information.
So far my net search for this has turned up nothing. I am hoping it is
simply because I'm not using the proper termnology when doing my search. If
you can tell me the proper termnology for this sort of thing, that would be
of great help. Or, better yet, if you could give URLs to where this stuff
is located, that would be fantastic!
Thanks in advance!

You may have more success with

"raven => black + bird"

rather than

"raven = black & bird"

Where => is intended to be the "implies" sign in logic. Ignoring the
subtleties mentioned by many of the others, this is now true and is not
contradicted by the fact that there are black birds which are not
ravens. = is symmetric i.e. if a = b then b = a. => is not symmetric
if a => b then it is possible that b => is not true. Sadly, assuming
b => a from a => b is a common mistake.

Provided the statements are quite simple, you can phrase them like this
and perform some useful mathematical analysis and make some deductions.
Use rules of logic such as if a => b and b => c then a => c. Books on
elementary logic should be useful.

However, remembering the comments by the others, even this approach
fails when given more real world statements in which the meaning of
words depends on the context (including non-linguistic context).
Natural language is too far from mathematical logic.

--
Seán O'Leathlóbhair

[j***@yahoo.com]

Post by Scott Jensen
I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.
"The raven is a black bird."
"raven = black + bird"
The idea being that you could take a document, use the rules to translate
the English sentences into math equations, and distill it down into its
informational parts and total them for what the document equaled in
information.
So far my net search for this has turned up nothing. I am hoping it is
simply because I'm not using the proper termnology when doing my search. If
you can tell me the proper termnology for this sort of thing, that would be
of great help. Or, better yet, if you could give URLs to where this stuff
is located, that would be fantastic!
Thanks in advance!

You may have more success with

"raven => black & bird"

rather than

"raven = black + bird"

Where => is intended to be the "implies" sign in logic. Ignoring the
subtleties mentioned by many of the others, this is now true and is not
contradicted by the fact that there are black birds which are not
ravens. = is symmetric i.e. if a = b then b = a. => is not symmetric
if a => b then it is possible that b => is not true. Sadly, assuming
b => a from a => b is a common mistake.

Provided the statements are quite simple, you can phrase them like this
and perform some useful mathematical analysis and make some deductions.
Use rules of logic such as if a => b and b => c then a => c. Books on
elementary logic should be useful.

However, remembering the comments by the others, even this approach
fails when given more real world statements in which the meaning of
words depends on the context (including non-linguistic context).
Natural language is too far from mathematical logic.

--
Seán O'Leathlóbhair

[Robert]

It was tried, but in a complete other way. They developed rules like
sentence = noun phrase(NP) + verbal phrase
noun phrase = article + adjective + nomen
verbal phrase = verb + noun phrase

But they(i have forgotten who) nevder did this on the level of meaning,
because you can never say anything without using context knowledge. If
you are more intrested in this topic I can suggest you read

Singer, M. (1990). Psychology of language: An introduction to sentence
and discourse processes.
There he gives a very detailed explanation how it was tried to modell
the language in a mathematical way and how they failed.
Hope it helps
Robert

Post by j***@yahoo.com

Post by Scott Jensen
I am interested to know if anyone has developed mathematical
translation rules that takes English sentences and converts them into
equations that produce a sum. Or if someone has done it for another
language and an English version of the rules has been done.
"The raven is a black bird."
"raven = black + bird"
The idea being that you could take a document, use the rules to
translate the English sentences into math equations, and distill it
down into its informational parts and total them for what the
document equaled in information.
So far my net search for this has turned up nothing. I am hoping it
is simply because I'm not using the proper termnology when doing my
search.

If

Post by Scott Jensen
you can tell me the proper termnology for this sort of thing, that
would

be

Post by Scott Jensen
of great help. Or, better yet, if you could give URLs to where this
stuff is located, that would be fantastic!
Thanks in advance!

You may have more success with
"raven => black & bird"
rather than
"raven = black + bird"

[Scott Jensen]

Post by Robert
Singer, M. (1990). Psychology of language: An introduction
to sentence and discourse processes.
There he gives a very detailed explanation how it was tried
to modell the language in a mathematical way and how they
failed.
Hope it helps

Thanks! I will get that book.

Scott Jensen

[Pavel314]

Post by Scott Jensen
I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.
"The raven is a black bird."
"raven = black + bird"

Your question reminds me of several courses in symbolic logic which I took
back in college where we did that sort of thing. Qualities were symbolized,
like BI(x) to mean "x is a bird" and BL(x) to mean "x is black."

Your statement above would be translated as RV(x) ==> BI(x) & BL(x), if x is
a raven then x is a bird and x is black. This is not the logical equivalent
to saying "If x is a bird and x is black then x is a raven".

Then there were the quantifiers, the existential quantifier E(x) meaning
"there exists an x" and the universal quantifier A(x) meaning "for all x".
(In the book, the E was written backwards and the A upside down, but I have
limited font here.) Google "universal quantifier" to get some links to the
subject. I remember doing lots of fun things with these. For example, your
statement might translate as:

A(x) [ RV(x) ==> BI(x) & BL(x) ] ==> E(x) [ BI(x) & BL(x) & RV(x) ]

There were formal rules for manipulating the quantifiers and qualifiers,
most of which I've forgotten long ago. Try asking for help on sci.logic or
sci.math.symbolic.

Paul

[Chris Croughton]

On Tue, 9 May 2006 20:26:30 -0400, Pavel314

Post by Pavel314
Your question reminds me of several courses in symbolic logic which I took
back in college where we did that sort of thing. Qualities were symbolized,
like BI(x) to mean "x is a bird" and BL(x) to mean "x is black."
Your statement above would be translated as RV(x) ==> BI(x) & BL(x), if x is
a raven then x is a bird and x is black. This is not the logical equivalent
to saying "If x is a bird and x is black then x is a raven".
Then there were the quantifiers, the existential quantifier E(x) meaning
"there exists an x" and the universal quantifier A(x) meaning "for all x".
(In the book, the E was written backwards and the A upside down, but I have
limited font here.)

More to the point, the rest of us have limited fonts as well (I would be
surprised if Unicode doesn't have the backward E and upside-down A, but
I don't have any font which could cope).

Post by Pavel314
Google "universal quantifier" to get some links to the
subject. I remember doing lots of fun things with these. For example, your
A(x) [ RV(x) ==> BI(x) & BL(x) ] ==> E(x) [ BI(x) & BL(x) & RV(x) ]

The sad thing is that I read that straight off and understood it, and I
haven't done symbolic logic for almost 30 years. It seams that I do
still use it internally even though I've forgotten most of the names of
things (I am frequently annoyed at the number of people who think that
[A => B] => [B => A])...

Post by Pavel314
There were formal rules for manipulating the quantifiers and qualifiers,
most of which I've forgotten long ago. Try asking for help on sci.logic or
sci.math.symbolic.

Converting a natural language into symbolic logic, which seems to be
what the OP is wanting to do, is however not generally possible. In
natural language it is possible, even easy, to say things which make no
sense, like the canonical "This sentence is a lie" which caused a lot of
computers in Star Trek to blow up, which are not possible to express in
symbolic logic without an obvious error. And there are ambiguities like
"time flies like an arrow" which can't be parsed mechanically without
extra information (although not all languages are as bad, that phrase in
an inflected language like Latin is not ambiguous).

[Note followup, if you override it please indicate in which newsgroup
you are reading this post.]

Chris C

[Burton Samograd]

Post by Chris Croughton
On Tue, 9 May 2006 20:26:30 -0400, Pavel314
More to the point, the rest of us have limited fonts as well (I would be
surprised if Unicode doesn't have the backward E and upside-down A, but
I don't have any font which could cope).

Try looking at LaTeX (actually TeX, but LaTeX is a much easier to
manage subset of the TeX language). It was designed for creating print
ready documents and is the standard tool for mathematicians
typesetting equations, papers and documents. It's generally not
WYSIWYG, but when combined with the emacs editor and specific LaTeX
packages, you can get a very powerful document and equation editor.

Although this doesn't help in the general case of writing by everyone,
it does help in the specific case of creating documents for reading by
others.

Post by Chris Croughton

Post by Pavel314
Google "universal quantifier" to get some links to the
subject. I remember doing lots of fun things with these. For example, your
A(x) [ RV(x) ==> BI(x) & BL(x) ] ==> E(x) [ BI(x) & BL(x) & RV(x) ]

The sad thing is that I read that straight off and understood it, and I
haven't done symbolic logic for almost 30 years. It seams that I do
still use it internally even though I've forgotten most of the names of
things (I am frequently annoyed at the number of people who think that
[A => B] => [B => A])...

Post by Pavel314
There were formal rules for manipulating the quantifiers and qualifiers,
most of which I've forgotten long ago. Try asking for help on sci.logic or
sci.math.symbolic.

Pick up a book discreet mathematics, they cover all of these things
and they are pretty cheap since they're a standard course in most
science curriculums.

Post by Chris Croughton
Converting a natural language into symbolic logic, which seems to be
what the OP is wanting to do, is however not generally possible. In
natural language it is possible, even easy, to say things which make no
sense, like the canonical "This sentence is a lie" which caused a lot of
computers in Star Trek to blow up, which are not possible to express in
symbolic logic without an obvious error. And there are ambiguities like
"time flies like an arrow" which can't be parsed mechanically without
extra information (although not all languages are as bad, that phrase in
an inflected language like Latin is not ambiguous).

Yes, it's very easy to create meaningless (as in having no true or
false value) sentances using any language (even symbolic logic and
mathematics). Mathematics is about finding and eliminating those
practices in the search of obtaining 'truth' (or at least truthful
axioms from which a 'real' version of truth can be built). Of course,
there is always a measure of faith (see Godel's Incompleteness
Theorem, The Halting Problem, or the various other limits to logical
truth and knowledge that have been found in other fields of study)
that is required before truth is accepted though, so really, nothing
can be proven to be true.

[Chris Croughton]

On Wed, 10 May 2006 10:25:18 -0600, Burton Samograd

Post by Burton Samograd

Post by Chris Croughton
On Tue, 9 May 2006 20:26:30 -0400, Pavel314
More to the point, the rest of us have limited fonts as well (I would be
surprised if Unicode doesn't have the backward E and upside-down A, but
I don't have any font which could cope).

Try looking at LaTeX (actually TeX, but LaTeX is a much easier to
manage subset of the TeX language). It was designed for creating print
ready documents and is the standard tool for mathematicians
typesetting equations, papers and documents. It's generally not
WYSIWYG, but when combined with the emacs editor and specific LaTeX
packages, you can get a very powerful document and equation editor.

I know LaTeX (and InfoTeX, and MusiTeX), but it isn't a font which can
be used with a news client, which was the point. Messages could be
posted in Unicode (or preferably UTF-8) which could convey the
appropriate characters but few people would be able to display them (and
my Xterms will only handle Latin-1 anyway).

Post by Burton Samograd
Although this doesn't help in the general case of writing by everyone,
it does help in the specific case of creating documents for reading by
others.

I would be surprised if the major technical text preparation packages
(I'm not includinf MS Word in those!) couldn't handle the extra
characters, and for most people they are easier than the TeX variants.

Post by Burton Samograd

Post by Chris Croughton

Post by Pavel314
Google "universal quantifier" to get some links to the
subject. I remember doing lots of fun things with these. For example, your
A(x) [ RV(x) ==> BI(x) & BL(x) ] ==> E(x) [ BI(x) & BL(x) & RV(x) ]

The sad thing is that I read that straight off and understood it, and I
haven't done symbolic logic for almost 30 years. It seams that I do
still use it internally even though I've forgotten most of the names of
things (I am frequently annoyed at the number of people who think that
[A => B] => [B => A])...

Post by Pavel314
There were formal rules for manipulating the quantifiers and qualifiers,
most of which I've forgotten long ago. Try asking for help on sci.logic or
sci.math.symbolic.

Pick up a book discreet mathematics, they cover all of these things
and they are pretty cheap since they're a standard course in most
science curriculums.

Depends where you are whether you can get textbooks cheaply. In the UK
they tend to be a lot more expensive than fiction books of the same
size...

Post by Burton Samograd

Post by Chris Croughton
Converting a natural language into symbolic logic, which seems to be
what the OP is wanting to do, is however not generally possible. In
natural language it is possible, even easy, to say things which make no
sense, like the canonical "This sentence is a lie" which caused a lot of
computers in Star Trek to blow up, which are not possible to express in
symbolic logic without an obvious error. And there are ambiguities like
"time flies like an arrow" which can't be parsed mechanically without
extra information (although not all languages are as bad, that phrase in
an inflected language like Latin is not ambiguous).

Yes, it's very easy to create meaningless (as in having no true or
false value) sentances using any language (even symbolic logic and
mathematics).

The thing is that "time flies like an arrow" is not meaningless, its
syntax is just ambiguous, because English syntax (and that of other
natural languages) has grown organically and hasn't been designed.
Lojban and a few other created languages are unambiguous, but few people
speak those and even fewer do so in normal conversation or writing.

Post by Burton Samograd
Mathematics is about finding and eliminating those
practices in the search of obtaining 'truth' (or at least truthful
axioms from which a 'real' version of truth can be built). Of course,
there is always a measure of faith (see Godel's Incompleteness
Theorem, The Halting Problem, or the various other limits to logical
truth and knowledge that have been found in other fields of study)
that is required before truth is accepted though, so really, nothing
can be proven to be true.

"In [pure] mathematics we never know what we are talking about nor
whether what we say is true." Mathematics has no direct connection to
things in the Real World(tm), at best it is a model of RW events but
since we don't have total information on the RW events it is an
idealised model. That's not saying that it has no use, even flawed and
incomplete models can be very useful, but the mathematicial always has
an 'out', and excuse, that the model is not the Real World(tm) thing
which it emulates...

Chris C

[Burton Samograd]

Post by Chris Croughton
On Wed, 10 May 2006 10:25:18 -0600, Burton Samograd

Post by Burton Samograd
Try looking at LaTeX (actually TeX, but LaTeX is a much easier to
manage subset of the TeX language). It was designed for creating print
ready documents and is the standard tool for mathematicians
typesetting equations, papers and documents. It's generally not
WYSIWYG, but when combined with the emacs editor and specific LaTeX
packages, you can get a very powerful document and equation editor.

I know LaTeX (and InfoTeX, and MusiTeX), but it isn't a font which can
be used with a news client, which was the point. Messages could be
posted in Unicode (or preferably UTF-8) which could convey the
appropriate characters but few people would be able to display them (and
my Xterms will only handle Latin-1 anyway).

Sorry, I must have missed the point :) I thought he (you? sorry, can't
see the original post) was asking for a way to typesetting
mathematics. I also have been trying to solve the problem of
displaying Unicode/UTF-8 with some success, but I mostly live in the
linux console (by choice) and there's an even greater number of of
twisty passages to follow on trying to get that problem solved.
Firefox and newer systems seem to be able to display multibyte
characters ok, as well as MathML, although I'm sure about the
newsclient.

Post by Chris Croughton

Post by Burton Samograd
Although this doesn't help in the general case of writing by everyone,
it does help in the specific case of creating documents for reading by
others.

I would be surprised if the major technical text preparation packages
(I'm not includinf MS Word in those!) couldn't handle the extra
characters, and for most people they are easier than the TeX
variants.

Yes, they would be easier I agree, but early ease of use leads to later
hitting limits and frustration, IMHO.

Post by Chris Croughton

Post by Burton Samograd
Pick up a book discreet mathematics, they cover all of these things
and they are pretty cheap since they're a standard course in most
science curriculums.

Depends where you are whether you can get textbooks cheaply. In the UK
they tend to be a lot more expensive than fiction books of the same
size...

I just go to the library and haven't bought a textbook in 10 years...

Post by Chris Croughton

Post by Burton Samograd
Yes, it's very easy to create meaningless (as in having no true or
false value) sentances using any language (even symbolic logic and
mathematics).

The thing is that "time flies like an arrow" is not meaningless, its
syntax is just ambiguous, because English syntax (and that of other
natural languages) has grown organically and hasn't been designed.
Lojban and a few other created languages are unambiguous, but few people
speak those and even fewer do so in normal conversation or writing.

I would not say the syntax is ambiguous in that sentance, but the
schemantics is. Logical languages do not included the a term 'like';
the evaluation of a word in an expression has to have an unambiguous
value to give it truth value or meaning (as in computer lanaguages).
That sentance 'does not compute', but it does make sense and have
meaning.

We understand the sentence because we are not computers (aka logic
machines). Some of us find logic very appealing, but it is not
'natural' in the sense of we are naturally born that way; logic was a
creation of man that we are taught. And yes, unambiguous languages
are very difficult to converse and write in but they are possible to
define and analyse, which is of interest to linguists that are trying
to analyse natural languages.

Post by Chris Croughton

Post by Burton Samograd
Mathematics is about finding and eliminating those
practices in the search of obtaining 'truth' (or at least truthful
axioms from which a 'real' version of truth can be built). Of course,
there is always a measure of faith (see Godel's Incompleteness
Theorem, The Halting Problem, or the various other limits to logical
truth and knowledge that have been found in other fields of study)
that is required before truth is accepted though, so really, nothing
can be proven to be true.

"In [pure] mathematics we never know what we are talking about nor
whether what we say is true." Mathematics has no direct connection to
things in the Real World(tm), at best it is a model of RW events but
since we don't have total information on the RW events it is an
idealised model. That's not saying that it has no use, even flawed and
incomplete models can be very useful, but the mathematicial always has
an 'out', and excuse, that the model is not the Real World(tm) thing
which it emulates...

Computers are machines that we have built to manipulate numbers. The
more we learn to use them, the closer we are getting to creating a
simulation/representation of a world (similar to) that we live in
(witness the current crop of Online Role Playing games which are
virtual words). We are building a universes from the 'atoms' up, and
we posess the source code.

We were born in a world that was here long ago. We became smarter,
created numbers, and started to notice patterns between physical
actions and interactions, which lead to the many fields of
mathematics. We were never given the source code for the world.

Mathematics, to me, is the reverse engineering of the world and
reality to find the source code. If you've ever looked at the code
base of a large software project, you would know that you really have
to combine both faith and observation to really belive that any system
could really work at all :)

[c***@yahoo.com]

Post by Scott Jensen
I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.
[snip]

Are you looking for something that will make the meaning of the
sentence easy to find? Prove that certain sentences are gibberish?
Tease out underlying hidden meanings?

Fifty years ago, general semantics was important to some, and used by
some to boil down political (and other) screeds to see what had really
been said.
http://www.general-semantics.org/about.htm

Cece

[Bill Bonde ('The path is clear, though no eyes can see')]

Post by Scott Jensen
I am interested to know if anyone has developed mathematical translation
rules that takes English sentences and converts them into equations that
produce a sum. Or if someone has done it for another language and an
English version of the rules has been done.
"The raven is a black bird."
"raven = black + bird"

How would this work for something beyond the copula? And how is that a
'sum'?

Post by Scott Jensen
The idea being that you could take a document, use the rules to translate
the English sentences into math equations, and distill it down into its
informational parts and total them for what the document equaled in
information.
So far my net search for this has turned up nothing.

Read back the previous bit of quoted paragraph and ask why that might
be.

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