This paper sets out my current ideas about natural language.

Lately I have been thinking about why natural language was developed by
evolution and why (as with other facets of its invention) don't the 
details matter much, i.e., there is English and Japanese and ...

Although I do not subscribe to the idea of 'deep structure' per se I am
curious about 1) why there are many languages and 2) in what sense can
(and do) we learn a new one. 

I have also been bothered by the question: What is the principle in
mathematics we use to move between what logicians call the elementary
and non-elementary theories of something (eg groups) 

This dual characterization of things manifests itself in natural language
all the time.  We say 'I have a red ball' and 'my ball is red'.  The word
'red' in this example is a property/predicate in the first case and is
a the 'name' of a color in the second.

If you look at a mathematics book (say Birkoff and McLane that describes
group theory) it frequently starts with listing the 'elementary' axioms
of group and proves some properties.  But soon it beging talking about
the order of a group (how many elements it has) and that the order of a
'subgroup' divides the order of a group.  This latter statement cannot
be expressed in the elementary theory of groups and, given that it mentions
both both non-elementary properties of groups and numbers the question is
where (and how) did we justify this shift of perspective? What principle
did we use and in where (was it stated and used)?

The Punch Line

I believe that language is built around things
  Things are either 'specific' objects or
  Non-Empty aggregrate of objects

The only building blocks of thought are the 'mental images' we have
of things.

I ask about things what 'type' of thing it is
  (in fact I believe that ALL things are aggrigates but we have the
  ability to 'freeze' an aggregate into a 'thing' (more later))

Language has survival value. It facilitates conversations between individuals
to determine when and if 1) their 'mental images' of things are comprable and 
2) if these 'mental images' actualy provide a reliable understanding of the
world outside our heads (the 'real' world???)

What are our 'mental images' of things like?  Well

A thing can have properties
  properties of things can have values (which are also things)
A thing can have parts

These properties, values and parts are themselves things that have 'types'. 
Furthermore they are 'mental' images so the must be fimite becsuse they
are physically located IN out heads.

Language allows us to describe things and relations among things

Things can be catoragizes by their properties (Leibnitz).
A category of things can be called its type.

Things can always be be described in more detail so there are no
individual things only catagories of things that can be made more
specific by refinement, ie, either 1) specializing some property or
part; or 2) adding a new property or part.

Two things that have the same properties are the same.  (Leibnitz)
Equality is therefore relative to the properties a object may have.

What is a relation?
  A Relation among things is itself a thing.
  A relation is something
  A relation is some thing
  An action is something tht takes place ovet time.
  An action is some thing tht takes place ovet time.
  One type of action has a description as a relation which 
    holds between the valuse of a thing's properties before the action
    and the values of a things properties after the action 
  Note: we mentioned that a thing maight change
    What do we mean by that? (Ganges)
  An operation is something that applys to an aggrate of things
    and produces something. In the language of logic an operation is 
    reepresented as a function symbol. In natural language we speak 
    of 'the effect' (note the definite article (ie it's a noun/thing))
    of an action.
  Another kind of action starts with some things and makes a 'new' thing.
    We might call this an imaginative action

The property of a thing is itself a thing
 (The notion of a higher order 'thing' needs discussion)

The properties of a thing implicitly define a language for discussing 
a thing and relations extends this to being able to talk about more
than one thing at a time

Our ability to 'understand' some thing is related to our ability to 
articulate thing about it.

Every example determines the elementary theory of the thing
 
A collection of things determines its non-elementary theory
A collection only containing a single example determines
  the non-elementary theory of the example.

Thus every object determines both its elementary and non-elementary
theory.

Narural Languageis the tool we use to describe objects and relations
between objects to someone else. We use both verbal and non-verbal 
language to relate our ideas.


A proposal for building a computer artifact that than think
-----------------------------------------------------------

Some considerations and requirements for making such an artifact can be
found [here].

Our proposal contains several parts

1) A description of data structures for 'mental models' - IBML types
2) A description of our 'mental model' of a 'thepry' - FOL contexts
3) A blusprint for a thinker 
4) A description for how this thinker can use language to comunicate
   and learn ideas.

1. Data Structures for 'mental images'

We propose using IBML types to as data structures

2) Our 'model' of a theory

FOL contexts.

3) Building a thinker

The creating subject.

4) Conversation

We need to be able to speak in order to describe thoughts using language and
to listen to inputs from our environment.  Although we will concentrate on
hearing naural language utterances, real thinkers habe other kinds of input,
eg, ambient noise.

Once we take as our goa; the construction of an autonomous thinker, our idea
of the meaning and function of natural language utterances changes.  We make

The meaning of an utterance is the change that hearing it has on a hearer.

This means that utterances (or sentenses) don't have mesning except as 
interpreted by a listener.

Data vs Capta

There is some good news. Our computer individual could converse using a nore
structured language than natural languade. This means that we can strat by
allowing conversation using descriptions of things that are immediately 
representative of its mental images.  


4.1 Linguistics

A description of our 'mental model' of a 'thepry'.
We use determiners to tell us if a thing is an example or a type in a
context.

       The ball - refers to a specific example of a ball
       A ball - refers to something of type ball

(|type| [ball] |subtype| [object]
   (|shape| .  |spherical|)
   (|diameter| . [inches])
) 

(|type| [inches] |subtype| [unit]
   (|size| [rational])
) 

(|example| |b|b |isa| [ball]
  (|diameter| . (6 in))
)



(if (is-an-example-of |b| [ball]) (type-of |b| [ball]))
(BALL? |b|)
(EQUAL (shape |b) |spherical|)
(SPHERICAL |b|)    

Language has several ways of describing things
  b [is a] ball
  b [is a] red ball


(example |red| example-of [color])
(type [color] subtype [term]
  (|name| {|red| |blue| |green|}) )

(|type| [sphere] |subtype [3d-geometrical-object]
  (|location| [3d-point])
  (|radius| [inches])
)

(|type| [ball] |subtype| [sphere]
  (color [color])
)

(type ,[typename] opt{subtype [typedesc]} @listOf[attdesc])
  (att1 :type ,[typedesc]1)
  (att2 :type ,[typedesc]2)
    ...
  (attn :type ,[typedesc]n)
)

(implies (equal atti o) (isa o [typedef]))

The non-elementary pivot is

 (INDVAR ex [typename]}
 (forall (ex)(implies (value ex Atti obj) (isin obj [typedef])) )

If [typename] is a [nameable-type] and
  
 (and
  (example-of ex [typename])
  (name ex name)
 )

then we get the nonelementary theory of   

Narrative

U1 "Nuclear factor-kappaB (NF-kappaB) is constitutively activated in diverse human malignancies by mechanisms that are not understood."

U2 "The MUC1 oncoprotein is aberrantly overexpressed by most human carcinomas and, similarly to NF-kappaB, blocks apoptosis and induces transformation.

u3 "This study demonstrates that overexpression of MUC1 in human carcinoma cells is associated with constitutive activation of NF-kappaB p65.

U4 "We show that MUC1 interacts with the high-molecular-weight IkappaB kinase (IKK) complex in vivo and that the MUC1 cytoplasmic domain binds directly to IKKbeta and IKKgamma."

U5 "Interaction of MUC1 with both IKKbeta and IKKgamma is necessary for IKKbeta activation, resulting in phosphorylation and degradation of IkappaBalpha.

U6 "Studies in non-malignant epithelial cells show that MUC1 is recruited to the TNF-R1 complex and interacts with IKKbeta-IKKgamma in response to TNFalpha stimulation."

U7 "TNFalpha-induced recruitment of MUC1 is dependent on TRADD and TRAF2, but not the death-domain kinase RIP1."

U8 "In addition, MUC1-mediated activation of IKKbeta is dependent on TAK1 and TAB2."

U9 "These findings indicate that MUC1 is important for physiological activation of IKKbeta and that overexpression of MUC1, as found in human cancers, confers sustained induction of the IKKbeta-NF-kappaB p65 pathway."



U1 "Nuclear factor-kappaB (NF-kappaB) is constitutively activated in diverse human malignancies by mechanisms that are not understood."

   >
X is constitutively activated by Y
X was killed by Y

 
 |Nuclear factor-kappaB|
 |NF-kappaB|
 |activation|
   mods
   |constitutively|
 |malignancy|
   mods
   |diverse|
   |human|
 |mechanism|
   |understood| (|not|)

In the narrative context

  (*fact* @ (= |Nuclear factor-kappaB| |NF-kappaB|) )

  (*fact* (statement 
    (*subject* (mod
               (*adj* @ "that are not understood") )
      |mechanisms|)
    (*verb* (mod
              (*where* @ "in diverse human malignancies")
              (*how"  @ |constitutively|) )
       activates|)
    (*object* @ |NF-kappaB|)
  ) )



1) pastuerization vs 2) pastuerize

1 'is a noun' and 2 'is a verb' BUT
they also function as adjectives and adverbds

Pasteurization is the process ...
He took a class in pasteurization
The pasteurization of milk led to better health
Tp pasteurize is to ...
He pasreurizes milk regularly
He psteurized the milk yesterday
The action of psstuerizing a liquid is ...
pasteurized milk

The meaning of these words (and their parts) form a cluster of words
whose collective meaning is only vaguely captured by the assignment of 
parts of speech it each piece.

As far as Iknow there is no wrrd in English for this type of association.

[Term]s

We need to distinguish between our mental images of things and the worsd we 
use to describe them to ourselves and others.  It is the relation between 
there words and our mental images of things that I believe is the crux of
natural language understanding.

Example
-------

Consider [geography]

The vocabulary of [geography] has two parallel ways of naming things
  [physical geography] and [political geography]

  [Pysical Geography] refers to the physical properties the universe
  [Political Geography] refers to [government]s and their [ruler]s

Consider the idea of [country]

  [country]
    in [physical geography] (eg the place called |France|) 
      We went to France for vacation.
      [country]s are [region]s

    in [political geography] (eg a sovereign nation |France|) 
      France fought in World War II on both sides.
      [country]s are [political entity]s

In both cases we have used the [term] |France|.  Linguists call these two
different 'senses' of the word |France|.  We prefer to think of this as
using the same [term] to describe to different mental images. 

Dsambiguation is done by context.

Note: We use the expression [term] rather than 'word' because for us [term]s
can be made up of multiple words (and may even contain 'puncuation' marks).
For example the term |New York| is itself an object of interest distinct
from the words  |New| and |York|.  This allows us to mention objects that
have more than one 'word' in their 'name', e.g., |Chocolate Chip Cookie| or
|Stanford University|.