Date: July 19,2002
From: Dick McCullough
To:   Richard Latimer
Subject: dogz, dogs and quantifiers

I like your dogz,dogs notation.  It has an
intuitive appeal which I think can help to
clarify the distinctions of individual and
collective concepts.  My intent in this
note is to summarize the basic ideas.
I will use my simple dog example to keep
the discussion as concrete as possible. 
I will use KR, but it's so English-like
that I don't think it will be a problem
for you.

You will notice that my definitions of
dogz,dogs,dog differ from yours.  I have
done this on purpose, trying to clarify
the subtle distinctions.

1. dogz and dogs
#==============#
Consider two or more entities

	Dutchess has color=black, ...
	Dutchess do  bark=bark_1, ... done
	Reno has color=white, ...
	Reno do  bark=bark_2, ... done
	...

and three groups

	dogz is  any Dutchess or  Reno or  ...
	dogs is  all Dutchess and Reno and ...
	dog  ise Dutchess, Reno, ...

dogz is an exclusive/individual group.
dogs is an inclusive/collective group.
The groups dogz and dogs have the same units,
but the group-unit relation is different.
dog is a group with the group-unit relation
left unspecified.

NOTE:
Before our current discussion, I had always
considered dog to be the same as dogz.
My more usual KR notation is
  dogz isany Dutchess, Reno, ...
  dogs isall Dutchess, Reno, ...
  dog  ise   Dutchess, Reno, ...
The inverse relation is expressed as
  Dutchess, Reno, ... isalt dogz
  Dutchess, Reno, ... ismem dogs
  Dutchess, Reno, ... isa   dog


2. Quantifiers
#============#
Consider the quantifiers

	a
	all
	any
	no
	some
	the

and the groups

	dogz
	dogs
	dog

What is the meaning of expressions of the form

	quantifier group

e.g.,

	a   dog
	any dogs

You can supply your own answer to this question.


3. English
#========#
How does all this relate to ordinary English?
My gut reaction is

	English "dog"  is KR "dogz"
	English "dogs" is KR "dogs"

But maybe we need to translate individual phrases,
e.g.,

	English "a dog"   is KR "a dogs"
	English "any dog" is KR "a dogz"

You can supply your own answer to this question.


4. Final Remarks
#==============#
It is sometimes helpful to think of dogz,dogs,dog
as abstract algebraic entities which represent
the solutions to equations, i.e., the answers to
questions.  For example,

	x do bark done ?
	x is dogz

NOTE:
The usual KE interaction for this example is

	...
	<myview:.=myconcept> ? do bark done
	# question <? do bark done>
	Dutchess do bark=bark_1 done
	Reno do bark=bark_2 done
	...


I have left significant unanswered questions here,
which could provide the basis for some interesting
future discussions.
I hope I have provided a clear foundation for
expressing answers to those questions.