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From: zuhair on 7 May 2010 17:46
On May 7, 9:50 am, Marshall <marshall.spi...(a)gmail.com> wrote:
> On May 7, 1:50 am, zuhair <zaljo...(a)gmail.com> wrote:
>
>
>
> > This syntax is both elegant, abbreviating and easily
> > readable.
>
> Maximizing abbreviation has the opposite effect as improving
> readability.

Agreed, but with training this would minimize, on the other
hand I am not claiming that improving readability is due
to the abbreviation power of this notation, the improvement comes
from removing crowded symbols like brackets, and membership
symbol and the universal quantifier symbol, which are the most
repeated symbols in most formulae, also the symbols here
are simpler than the more complex symbols used in standard
method, for example, symbols given to disjunction, conjunction
and implication all use two characters, while they are using
at most one character here.

The quantifiers are odd looking symbols, the universal quantifier
is an upside-down A symbol, and I see no creative act in that at all,
while the existential quantifier is a rotated E ( a turnaround E)
symbol,
both look ugly and bizarre, beside they are complex symbols
containing many angles and can be viewed as combination
of many smaller symbols, while at the same time the are suppose
to denote simple concepts. The way how these symbols are written
in standard books is totally unacceptable, there is no rational behind
such odd characters.

(the mirror letters in English, like p and q , are pretty much known
symbols and there is no problem with them, n and u
are both inverted-rotated symbols, but still they are elegant, but
the inverted A and the rotated E are very bizarre, they are simply
not edible)
>
> >   The standard notation appears as too long,
> >  crowded, boring, and clumsy by comparison, that is
> >  besides it contains inverted symbols and
> >  rotated symbols without an obvious justification.
>
> The standard notation is already quite terse, to the
> point that compressing it further strikes me as a bad
> idea.

hmmm.........
>
> The symbols you describe as rotated aren't. Does the
> English alphabet contain rotated symbols? I would say
> not, and yet lowercase u and n are the same modulo
> rotation.

Yes of course, p and q are examples, also as you mentioned
n and u are actually inverted-rotated symbols. However upper-case
English don't have that phenomena, and as I said above
an inverted Capital A and a rotated Capital E are indeed ugly
symbols.
>
> The "shortening" of the implication arrow to a greater-than
> symbol is an ASCII-specific optimization. The right arrow
> is a single symbol in unicode, and when written by hand.
> Also, this makes is difficult/ambiguous to write anything
> involving numeric comparison. This may not be a goal
> of yours, but it is a common application of standard
> notation.
>
> > In my personal opinion the above record is the *best way
> > of writing first order logic with identity and membership*,
> > known thus far!
>
> "Best" is relative to a given set of requirements, and
> any design is going to involve making tradeoffs.

Agreed.
>
> Marshall

Thanks for your positive contribution here.

Zuhair

From: zuhair on 7 May 2010 20:16
On May 7, 9:50 am, Marshall <marshall.spi...(a)gmail.com> wrote:
> On May 7, 1:50 am, zuhair <zaljo...(a)gmail.com> wrote:
>
>
>
> > This syntax is both elegant, abbreviating and easily
> > readable.
>
> Maximizing abbreviation has the opposite effect as improving
> readability.
>
> >   The standard notation appears as too long,
> >  crowded, boring, and clumsy by comparison, that is
> >  besides it contains inverted symbols and
> >  rotated symbols without an obvious justification.
>
> The standard notation is already quite terse, to the
> point that compressing it further strikes me as a bad
> idea.
>
> The symbols you describe as rotated aren't. Does the
> English alphabet contain rotated symbols? I would say
> not, and yet lowercase u and n are the same modulo
> rotation.
>
> The "shortening" of the implication arrow to a greater-than
> symbol is an ASCII-specific optimization. The right arrow
> is a single symbol in unicode, and when written by hand.
> Also, this makes is difficult/ambiguous to write anything
> involving numeric comparison. This may not be a goal
> of yours, but it is a common application of standard
> notation.
>
> > In my personal opinion the above record is the *best way
> > of writing first order logic with identity and membership*,
> > known thus far!
>
> "Best" is relative to a given set of requirements, and
> any design is going to involve making tradeoffs.
>
> Marshall

Just to add to what I wrote previously in reply to your really
positive notes, that I appreciate so much.

To me personally I see that there must be some kind of rational behind
notations. It is true that we can use any notation however bizarre
looking to write logic with as far as it is uniquely readable, but I
don't like that.

Logical symbols must be the simplest possible, they must not be
bizarre, they must not contain upside-down symbols or turnaround
symbols, there must be some kind
of explanation offered behind each symbol.

The system that I wrote have an explanation for each symbol in it.

~ to represent negation is an accurate symbol, the symbol have
opposing
characteristic the first bend is opposite the second one in direction,
and this
gives opposing impression and it is a good symbolism to represent
negation by a symbol that gives opposing impression, that's why I kept
this symbol
in my system.

Conjunction by juxtaposing the two *formulae*, is pretty much
intuitive since
juxtaposing formulae does indeed give the impression of conjunction.

Disjunction using the symbol "|" is also intuitive, since the symbol
"|"
is a boundary symbol giving the impression of a separator, and it is
pretty much intuitive to represent disjunction by a symbol that
implies
a kind of separation.

notice that conjunction and disjunction are symbolized using
non directional symbols, you see that | doesn't give any impression
of directionality, neither does juxtaposing formulae.

Implication, requires a directional symbol, because implication is a
directional
concept! and the simplest of which is > , there is no need for the
stem in -> at all,
this is a redundant notation, since > does the job nicely.

same goes for the bi-conditional.

On the other hand can you tell me the rational behind using a Large V
to represent
disjunction and an inverted Large V to represent conjunction, I see no
rational
behind such clumsy symbols at all.

Now the quantifiers.

I represented existential quantification by the symbol "_", this
symbol
gives and "expectational" impression, once you see the symbol _
you wander what is after it, and it is good to represent
existence by and expectational symbol.

Now regarding universal quantification, all what we want to say
in universal quantification say of x is "for Any x", this is best
represented by just writing x like that, this would give
the full impression of any x. no need for any symbol for this
quantifier.

Can you tell me what is the rational beyond an upside-down A
and a turnaround E?

Regarding using juxtaposition of terms (variables, constants and
functions)
to represent the membership relation, then this is evident, since the
principal primitive in fol(membership,=) is membership, and it would
be the most repeatable symbol, so it is better represented by
juxtaposing
the terms.

Identity relation is an ancient symbol, and it is consistent of two
bars
identical to each other, so it is OK.

The dot notation is much more neat than the bracket system, and it
has a good abbreviation power, and it is superior to be the bracket
system, and it is a proved notation since Principa Mathematica days.

The other rules of abbreviation are only based on simply concepts
derived from first order logic itself, and they help to remove the
bracket
and obviate the need for using excessive dot notation.

So in this system, there is rational beyond each symbol, and the net
result is a nice looking formulae, clear, not crowded and actually
the tell you the core of what is going on in the formulae, you can
see the skeleton of reasoning flowing in these formulae, so it strip
naked
what is going basically their in these formulae ,unlike
the traditional notation which serve to get you lost in the crowd.

So this notation is indeed in many aspects superior to the standard
one.

Zuhair







From: zuhair on 7 May 2010 20:33
On May 7, 9:50 am, Marshall <marshall.spi...(a)gmail.com> wrote:
> On May 7, 1:50 am, zuhair <zaljo...(a)gmail.com> wrote:
>
>
>
> > This syntax is both elegant, abbreviating and easily
> > readable.
>
> Maximizing abbreviation has the opposite effect as improving
> readability.
>
> >   The standard notation appears as too long,
> >  crowded, boring, and clumsy by comparison, that is
> >  besides it contains inverted symbols and
> >  rotated symbols without an obvious justification.
>
> The standard notation is already quite terse, to the
> point that compressing it further strikes me as a bad
> idea.
>
> The symbols you describe as rotated aren't. Does the
> English alphabet contain rotated symbols? I would say
> not, and yet lowercase u and n are the same modulo
> rotation.
>
> The "shortening" of the implication arrow to a greater-than
> symbol is an ASCII-specific optimization. The right arrow
> is a single symbol in unicode, and when written by hand.
> Also, this makes is difficult/ambiguous to write anything
> involving numeric comparison. This may not be a goal
> of yours, but it is a common application of standard
> notation.
>
> > In my personal opinion the above record is the *best way
> > of writing first order logic with identity and membership*,
> > known thus far!
>
> "Best" is relative to a given set of requirements, and
> any design is going to involve making tradeoffs.
>
> Marshall

Just to add to what I wrote previously in reply to your really
positive notes, that I appreciate so much.

To me personally I see that there must be some kind of rational
behind
notations. It is true that we can use any notation however bizarre
looking to write logic with, as far as it is uniquely readable, but
I don't like that.

Logical symbols must be the simplest possible, they must not be
bizarre, they must not contain upside-down symbols or turnaround
symbols, there must be some kind of explanation offered behind
each symbol.

The system that I wrote have an explanation for each symbol in it.

~ to represent negation is an accurate symbol, the symbol have
opposing characteristic, the first bend is opposite the second one in
direction,
and this gives opposing impression, and it is a good symbolism to
represent
negation by a symbol that gives opposing impression, that's why I
kept
this symbol in my system.

Conjunction by juxtaposing the two *formulae*, is pretty much
intuitive since juxtaposing formulae does indeed give the
impression of conjunction, and this was actually used before,
possibly traced to prinicipa Mathematica.

Disjunction using the symbol "|" is also intuitive, since the symbol
"|" is a boundary symbol giving the impression of a separator, and it
is
pretty much intuitive to represent disjunction by a symbol that
implies a kind of separation, since disjunction itself implies
a kind of separation.

notice that conjunction and disjunction are symbolized using
non directional symbols, you see that | doesn't give any impression
of directionality, neither does juxtaposing formulae.

Implication, requires a directional symbol, because implication is a
directional concept! and the simplest of which is > ,
there is no need for the stem in -> at all,
this is a redundant notation, since > does the job nicely.

same goes for the bi-conditional.

On the other hand can you tell me the rational behind using a Large V
to represent disjunction and an inverted Large V to represent
conjunction,
I see no rational behind such clumsy symbols at all.

Now the quantifiers.

I represented existential quantification by the symbol "_", this
symbol gives and "expectational" impression, once you see the symbol
_
you wander what is after it, and it is good to represent
existence by and expectational symbol.

Now regarding universal quantification, all what we want to say
in universal quantification say of x is "for Any x", this is best
represented by just writing x like that, this would give
the full impression of any x. no need for any symbol for this
quantifier.

If one insist that a symbol must be given to universal quantification,
then I would choose the symbol "\", since it gives the impression
of a general kind of introduction, and the generality impression of
the symbol make it eligible to represent the universal quantifier.

However I still insist that only writing x like that is better to
represent the meaning of "any x".

Can you tell me what is the rational beyond an upside-down A
and a turnaround E?

Regarding using juxtaposition of terms (variables, constants and
functions) to represent the membership relation, this is evident,
since the principal primitive in fol(membership,=) is membership,
and it would be the most repeatable symbol, so it is better be
represented by juxtaposing the terms.

Identity relation is an ancient symbol, and it is made up of two
bars identical to each other, so it is OK.

The dot notation is much more neat than the bracket system, and it
has a good abbreviation power, and it is superior to the bracket
system, and it is a proved notation since Principa Mathematica days.

The other rules of abbreviation are only based on simply concepts
derived from first order logic itself, and they help to remove the
brackets and obviate the need for using excessive dot notation.

So in this system, there is a rational beyond each symbol, and the
net
result is a nice looking formulae, clear, not crowded and actually
tell you the core of what is going on in the formulae, you can
see the skeleton of reasoning flowing in these formulae,
so it strip naked what is going on basically in these formulae ,
unlike the traditional notation which serve to get you lost in the
crowd.

So this notation is indeed in many aspects superior to the standard
one.

Zuhair
From: zuhair on 7 May 2010 20:43
On May 7, 9:50 am, Marshall <marshall.spi...(a)gmail.com> wrote:
> On May 7, 1:50 am, zuhair <zaljo...(a)gmail.com> wrote:
>
>
>
> > This syntax is both elegant, abbreviating and easily
> > readable.
>
> Maximizing abbreviation has the opposite effect as improving
> readability.
>
> >   The standard notation appears as too long,
> >  crowded, boring, and clumsy by comparison, that is
> >  besides it contains inverted symbols and
> >  rotated symbols without an obvious justification.
>
> The standard notation is already quite terse, to the
> point that compressing it further strikes me as a bad
> idea.
>
> The symbols you describe as rotated aren't. Does the
> English alphabet contain rotated symbols? I would say
> not, and yet lowercase u and n are the same modulo
> rotation.
>
> The "shortening" of the implication arrow to a greater-than
> symbol is an ASCII-specific optimization. The right arrow
> is a single symbol in unicode, and when written by hand.
> Also, this makes is difficult/ambiguous to write anything
> involving numeric comparison. This may not be a goal
> of yours, but it is a common application of standard
> notation.
>
> > In my personal opinion the above record is the *best way
> > of writing first order logic with identity and membership*,
> > known thus far!
>
> "Best" is relative to a given set of requirements, and
> any design is going to involve making tradeoffs.
>
> Marshall

I just wanted to add to what I wrote previously in reply to your
really
positive notes, that I appreciate so much.

To me personally I see that there must be some kind of rational
behind notations. It is true that we can use any notation however
bizarre looking to write logic with, as far as it is uniquely
readable,
but I don't like that.

Logical symbols must be the simplest possible, they must not be
bizarre, they must not contain upside-down symbols or turnaround
symbols, there must be some kind of explanation offered behind
each symbol.

The system that I wrote have an explanation for each symbol in it.

~ to represent negation is an accurate symbol, the symbol have
opposing characteristic, the first bend is opposite the second one in
direction, and this gives opposing impression,
and it is a good symbolism to represent negation by
a symbol that gives opposing impression, that's why I kept
this symbol in my system.

Conjunction by juxtaposing the two *formulae*, is pretty much
intuitive since juxtaposing formulae does indeed give the
impression of conjunction, and this was actually used before,
possibly traced to prinicipa Mathematica.

Disjunction using the symbol "|" is also intuitive, since the symbol
"|" is a boundary symbol giving the impression of a separator, and it
is pretty much intuitive to represent disjunction by a symbol that
implies a kind of separation, since disjunction itself implies
a kind of separation.

notice that conjunction and disjunction are symbolized using
non directional symbols, you see that | doesn't give any impression
of directionality, neither does juxtaposing formulae.

Implication, requires a directional symbol, because implication is a
directional concept! and the simplest of which is > ,
there is no need for the stem in -> at all,
this is a redundant notation, since > does the job nicely.

same goes for the bi-conditional.

On the other hand can you tell me the rational behind using a Large V
to represent disjunction and an inverted Large V to represent
conjunction, I see no rational behind such clumsy symbols at all.

Now the quantifiers.

I represented existential quantification by the symbol "_", this
symbol gives and "expectational" impression, once you see the symbol
_
you wander what is after it, and it is good to represent
existence by an expectational symbol.

Now regarding universal quantification, all what we want to say
in universal quantification say of x is "for Any x", this is best
represented by just writing x like that, this would give
the full impression of any x. no need for any symbol for this
quantifier.

If one insist that a symbol must be given to universal
quantification,
then I would choose the symbol "\", since it gives the impression
of a general kind of introduction, and the generality impression of
the symbol make it eligible to represent the universal quantifier.

However I still insist that only writing x like that is better to
represent the meaning of "any x".

Can you tell me what is the rational beyond an upside-down A
and a turnaround E?

Regarding using juxtaposition of terms (variables, constants and
functions) to represent the membership relation, this is evident,
since the principal primitive in fol(membership,=) is membership,
and it would be the most repeatable symbol, so it is better be
represented by juxtaposing the terms.

Identity relation is an ancient symbol, and it is made up of two
bars identical to each other, so it is OK.

The dot notation is much more neat than the bracket system, and it
has a good abbreviation power, and it is superior to the bracket
system, and it is a proved notation since Principa Mathematica days.

The other rules of abbreviation are only reflect simple quantification
concepts derived from first order logic itself, and they help to
remove the
brackets and obviate the need for using excessive dot notation.

So in this system, there is a rational beyond each symbol, and the
net result is a nice looking formulae, clear, not crowded and
actually
tell you the core of what is going on in the formulae, you can
see the skeleton of reasoning flowing in these formulae,
so it strip naked what is going on basically in these formulae,
unlike the traditional notation which serve to get you lost in the
crowd.

So this notation is indeed in many aspects superior to the standard
one.

Zuhair
From: zuhair on 7 May 2010 20:52
On May 7, 9:50 am, Marshall <marshall.spi...(a)gmail.com> wrote:
> On May 7, 1:50 am, zuhair <zaljo...(a)gmail.com> wrote:
>
>
>
> > This syntax is both elegant, abbreviating and easily
> > readable.
>
> Maximizing abbreviation has the opposite effect as improving
> readability.
>
> >   The standard notation appears as too long,
> >  crowded, boring, and clumsy by comparison, that is
> >  besides it contains inverted symbols and
> >  rotated symbols without an obvious justification.
>
> The standard notation is already quite terse, to the
> point that compressing it further strikes me as a bad
> idea.
>
> The symbols you describe as rotated aren't. Does the
> English alphabet contain rotated symbols? I would say
> not, and yet lowercase u and n are the same modulo
> rotation.
>
> The "shortening" of the implication arrow to a greater-than
> symbol is an ASCII-specific optimization. The right arrow
> is a single symbol in unicode, and when written by hand.
> Also, this makes is difficult/ambiguous to write anything
> involving numeric comparison. This may not be a goal
> of yours, but it is a common application of standard
> notation.
>
> > In my personal opinion the above record is the *best way
> > of writing first order logic with identity and membership*,
> > known thus far!
>
> "Best" is relative to a given set of requirements, and
> any design is going to involve making tradeoffs.
>
> Marshall

I just wanted to add to what I wrote previously in reply
to your really positive notes, that I appreciate so much.

To me personally I see that there must be some kind of rational
behind notations. It is true that we can use any notation however
bizarre looking to write logic with, as far as it is uniquely
readable, but I don't like that.

Logical symbols must be the simplest possible, they must not be
bizarre, they must not contain upside-down symbols or turnaround
symbols, there must be some kind of explanation offered behind
each symbol.

The system that I wrote have an explanation for each symbol in it.

~ to represent negation is an accurate symbol, the symbol have
opposing characteristic, the first bend is opposite the second one in
direction, and this gives opposing impression,
and it is a good symbolism to represent negation by
a symbol that gives opposing impression, that's why I kept
this symbol in my system.

Conjunction by juxtaposing the two *formulae*, is pretty much
intuitive since juxtaposing formulae does indeed give the
impression of conjunction, and this was actually used before,
possibly traced to prinicipa Mathematica.

Disjunction using the symbol "|" is also intuitive, since the symbol
"|" is a boundary symbol giving the impression of a separator, and it
is pretty much intuitive to represent disjunction by a symbol that
implies a kind of separation, since disjunction itself implies
a kind of separation.

notice that conjunction and disjunction are symbolized using
non directional symbols, you see that | doesn't give any impression
of directionality, neither does juxtaposing formulae.

Implication, requires a directional symbol, because implication is a
directional concept! and the simplest of which is > ,
there is no need for the stem in -> at all,
this is a redundant notation, since > does the job nicely.

same goes for the bi-conditional.

On the other hand can you tell me the rational behind using a Large V
to represent disjunction and an inverted Large V to represent
conjunction, I see no rational behind such clumsy symbols at all.

Now the quantifiers.

I represented existential quantification by the symbol "_", this
symbol gives an "expectational" impression, once you see the symbol
"_ ", you wander what is after it, and it is good to represent
existence by an expectational symbol.

Now regarding universal quantification, all what we want to say
in universal quantification say of x is "for Any x", this is best
represented by just writing x like that, this would give
the full impression of any x. no need for any symbol for this
quantifier.

If one insist that a symbol must be given to universal
quantification, then I would choose the symbol \
since it gives the impression of a general kind
of introduction, and the generality impression of
the symbol make it eligible to represent
the universal quantifier.

However I still insist that only writing x like that is better to
represent the meaning of "any x".

Can you tell me what is the rational beyond an upside-down A
and a turnaround E?

Regarding using juxtaposition of terms (variables, constants and
functions) to represent the membership relation, this is evident,
since the principal primitive in fol(membership,=) is membership,
and it would be the most repeatable symbol, so it is better be
represented by juxtaposing the terms.

Identity relation is an ancient symbol, and it is made up of two
bars identical to each other, so it is OK.

The dot notation is much more neat than the bracket system, and it
has a good abbreviation power, and it is superior to the bracket
system, and it is a proved notation since Principa Mathematica days.

The other rules of abbreviation only reflect simple quantification
concepts derived from first order logic itself, and they help to
remove the brackets and obviate the need for using
excessive dot notation.

So in this system, there is a rational beyond each symbol, and the
net result is a nice looking formulae, clear, not crowded and it
actually tell you the core of what is going on in the formulae, you
can
see the skeleton of reasoning flowing in these formulae,
so it strip naked what is going on basically in these formulae,
unlike the traditional notation which serve to get you lost in the
crowd.

So this notation is indeed in many aspects superior to the standard
one.

Zuhair
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