1.
Introduction
In 1985, Adi developed a theory of the Arabic
language by looking at an old Arabic book and asking a single question
thousands of times: "Do the many contexts in which a word is used point to
an invariant abstract parallel between the word structure and the structure of
the physical context to which the word refers?"
In Arabic, there is one-to-one correspondence
between letters and sounds. Arabic has
28 letters and four vowels. Most Arabic word stems are verbs and most of them
consist of three consonants. Vowels are
added in the course of creating words out of stems and short vowels are usually
not written. Short vowels are not even
considered letters. Even long
(stretched) vowels are sometimes not written.
Vowels do not change the basic meaning.
First, Adi examined the contextual usage of
prefixes, suffixes, prepositions, conjunctives, pronouns and other
morphological and syntactic units that consisted of a single consonant and a
vowel. Then he turned to stems that had
two soft consonants (ya, hamza, waw, ha). Soft consonants are related to vowels
and are known to add much less meaning to stems than other consonants. Then, he examined stems with one soft
consonant, and finally stems without soft consonants. Adi started by examining stems that denote simple processes that
are easy to visualize.
The Readware ontology, a framework of knowledge, was
the result of these analyses.
2. Arabic
Vowels and Consonants Point to Abstract Aspects
Adi observed that Arabic vowels and consonants
indicated different aspects of "things." In a refinement process, he chose a label for each abstract
aspect he encountered. In the examples
below, the abstract aspects are in bold type.
This is a big collection of examples and the reader
may not wish to read them all. The
formal presentation of the ontology follows.
More advanced examples will be discussed later on.
We start with vowels: vowel_i, vowel_a, vowel_u and sukoon. Short vowels at the end of Arabic nouns and verbs indicate
grammatical aspects. Among other
things, vowel_i indicates the inward aspect:
the dynamic aspect of closed, someone owning or receiving something. Vowel_a indicates that something is being acted upon: the open
aspect. Vowel_u indicates the engaged aspect: activeness for nouns and the pending tense
(mudari') for verbs. And sukoon (silence, the null vowel) indicates a special
condition for verbs: the separate
aspect.
Next we look at soft consonants (ya, hamza, waw, ha)
that are relatives of vowels (vowel_i, vowel_a, vowel_u, sukoon, respectively).
The address article "ya" (spelled ya and a
stretched vowel_a) is used to tell someone "this message is for you." It is a "closed assignment."
The "hamza" is a question article: the
matter is open.
The Arabic conjunctive "wa" (spelled waw)
means "and," "while" or "I swear an oath by..."
The meaning "and" engages
(connects) two things. The
"while" sense (as in "eating while talking") also expresses
engagement into something. An oath is an engagement (a commitment).
We find the consonant "ha" (pronounced
like "h") at the beginning of all third person pronouns
"hoowa" (he, spelled ha waw) "heeya" (she, spelled ha ya)
etc. The third person is a separate element. Element
is the static view of assignment.
Consider the consonants (mem, fa, dal, thal).
The single-consonant prefix "m-" (meem) is
used profusely in Arabic morphology to indicate a number of things: a person,
an activity, a time, a place, a method or an instrument. All these things are plausible realizations of the manifestation aspect. Some are dynamic such as activity and method, and others are static such as place and person. We
call the static aspect of manifestation a domain.
"Foo" (spelled fa waw) means
"mouth" (open domain) and "fee" (in, into,
spelled "faa ya") is an open
domain, too. There is a dynamic realization aspect to "open," namely "forward" that is indicated by the
"into" meaning of "fee" and also by the conjunctive
"fa" which means "then," a forward manifestation.
"Dal" indicates engaged domain or engaged manifestation as suggested by it being
the only non-soft consonant in "wadi" (valley, engaged domain), "diyah" (compensation--engaged manifestation--for involuntary
manslaughter) and "adaa" (paying back debt, engaged manifestation).
The consonant "thal" (pronounced like
"the") is combined with vowels to express a separate or unusual manifestation
(special attribute, this, that, the one who, that which, etc.). "Ithe" (spelled hamza thal) points
to a special (separate) time
"remember when..."
"Itha" (spelled hamza thal stretched vowel_a) means
"when": The hamza assigns a specific (separate) time (thal).
The consonant group ('ain, noon, qaf, ghain) indicates
the aspect of containment.
In "wi'a" (closed container, waw 'ain stretched vowel_a hamza),
"'ain" is the only non-soft consonant. The noon in "Ayna"
(hamza ya noon)--which means
"where"--indicates an open
containment. The stem "waw qaf
ya" means shielding, an engaged
containment. The stem "ghain ya ba" means to hide: separate containment. In the stems "Qaf dal ra"
(quantity) and "qaf waw meem" (straight), "qaf" indicates
the static view of containment: order.
There are four groups of abstract aspects:
boundary
conditions (static/dynamic): closed/backward, open/forward
engagement
conditions:
engaged, separate
views: static, dynamic
processes: assignment, manifestation, containment
static views
of processes: element, domain, order
Now consider the consonant group (ra, lam, ba,
ta). "lam" is a preposition
that means "belonging to," a forward
assignment to a domain. "Ba" is a preposition that expresses
causality, and engagement assignment
between manifestations. "Ta" is an oath preposition, a special assignment to a manifestation.
"Waraa," where "ra" is the only non-soft consonant means
"behind," a backward
assignment in domain. This group of
consonants combines assignment and manifestation.
We see a combination of order and element
(ordered elements, streams, structures) in the consonants (seen, zay, sad,
tha). For example, "seen waw ya" indicates
"equality" and "balance," a closed order of elements.
"Seen ya lam"
(flood) is closed containment of
elements.
The consonants (kaf, ddad, tta, kha) combine containment and domain. "Kam" (kaf meem) means "how
much" and "how many." "Ttawa" means "to
fold" (engaged containment of
domain). "Khawa" means
"empty" (separation of domain
and containment).
"Ddalla" means "losing one's way" (open order in
domain).
Finally, the "heavy" consonants (hha,
sheen, geem, zza) combine
assignment/element, manifestation/domain and containment/order. They are general purpose indicators.
"Hha ya waw" means
"life" (closed element domain
order). "Sheen ya hamza" means "thing" (open whatever). "geem ya hamza" means "to
come" (engage whatever).
"Zza lam lam" means "to remain" (to separate from whatever).
Adi combined boundary conditions with engagement
conditions in one dimension and all combinations of the three processes
(including having none) to create a 4 x 8 abstract matrix that is described in
section 4 below. All processes
contained in matrix elements can alternatively assume static views. Paul Prueitt wrote the following section in
an attempt to explain Adi's motivation for merging abstract dimensions.
3. The
Abstract Concept of a Framework
The notion of a framework is central to at least
three scholar’s works, Zachman, Sowa and Ballard. An Internet reference to these scholar’s work is given by
Prueitt [1]
Formal definition of the abstract framework: Let S1, S2, … , Sn be n
framework aspect sets. These sets may
have any allowable member, and are considered here to be finite and in fact
having only a few members. The
dimensions of the framework match the integer that is the number of framework
aspect sets. The size of the framework
is the integer that is the product of the size of all framework aspects
sets.
F = S1 x S2
x … x Sn
An abstract
framework is the cross product of the set of framework aspect sets.
For example, let A and B be two sets with size(A) =
m and size(B) = n. Then size(F) = m*n,
when
F = A x B
If A = (aspect1, aspect2) and B = (aspect3, aspect4,
aspect5), then the size(F) = 6.
F is often represented as a matrix, where the cells contain
the elements of the cross product. In
this case we have a 2x3 matrix
F = [ f(i,j) | i = 1,2 and j = 1,2,3 ]
The cell f(1,1) contains the ordered pair
(aspect1, aspect3), and so forth.
The dimensions of a framework are selected by a human mind as a coherent domain of inquiry with a specific set of descriptive elements like words or phrases. These descriptive elements should be selected as if the axioms of a specific geometry, i.e., each aspect of the dimensional description should be as independent as possible from the other aspects.
The set of aspects should “cover” a coherent domain
of inquiry. The set should be minimal
in number, only having a sufficient number of elements to serve the purpose of
description and conversation about the domain.
The independence and the sufficiency constraints will create a situation
where each element has the same “status”, in terms of importance. Each descriptive element is important and
necessary.
Coherence is related to completeness and
consistency. This is a deep discussion
with some simple consequences. The
process of separating the dimensions of an inquiry is quite natural and
occurring in all children’s minds as they make sense of the world. Coherence is not possible across all of the
experiences that we humans have. So the
selection of a coherent figure in a figure ground relationship in the
perception of reality is natural. We
see this in the development of the Adi Notational System as applied to the
structural ontology related to the Arabic language.
For example, the first dimension in the Adi construction is a cross product of two simple sets that must, seem to, lie at the base of any organization of data into a structured ontology. A structured ontology is stratified into layers of abstraction.
These two underlying sets are T and G:
T = {closed, open}
G = {self, engaged}
T the set of boundary circumstances and G is the set
of engagement conditions.
In the next section, the reader will see a
separation of the four elements of the cross product of T and G. This separation causes each element to be
considered without relationship to any other element. The literature on complex systems regards this isolation of
elements from the environment of these elements as indicative of a cross-scale transformation. In this case, the specific transform
operates from a high level of abstraction to a lower level of abstraction. Each level of abstraction has a unique set
of completeness and consistency constraints, these constraints being imposed by
the level of abstraction.
The movement from one level to another level changes
the formal definition of what a “formal system is”, what an “environment to a
systems is, and thus changes the expression of internal and external
relationships that are potential is possible expressions in the natural
world.
In a structured ontology, the levels of abstraction
have properties that we conjecture to be inherited from the physical
organization in a concrete reality existing in a present moment. The concrete reality in a present moment is
referenced linguistically using the word “pragmatic”. Meaning and form in the abstract do not have to be seated in a
pragmatic axis. Yet, it would seem
that, the search for truth does make this requirement for a ground truth.
Abstraction leads to a demand for coherence and
completeness, two conditions that Godel and others inform the scholars
about. Coherence and completeness
cannot co-exist in a formal abstract system.
This search for truth provides a possible grounding of abstraction in
the real world in real time. The
generating and use of natural language within a community of humans attempts
this same grounding. The non-coherence
in the natural world inhibits the search for a single truth. The dialectic is thus, perhaps seen as,
between singleness of mind and respect for others.
Our technology is designed to facilitate the
grounding of human perception over data structures in computer systems. In one case, the object of investigation is
about the cultural world and the assistance that natural language may provide
to grounding one’s understanding of aspects of the cultural world. Human-centric information production allows
the human to step-away-from the abstraction created by computing systems and
represented visually these abstractions as co-occurrence patterns. This stepping-away-from in called “mutual
induction”, since the machine provides cognitive priming and the human provided
the actually induction of new mental states.
The cross scale transform has an up and a down
movement. First a bag [2]
containing four elements is created.
The down movement leaves behind the global structure imposed by the two
dimensions. The bag contains the four
elements of the cross product but without any contextualization. Then the elements of this bag is ordered in
a different way, i.e. having now only one dimension rather than two. The up ward movement of the cross-scale
transform imposes an order to the contents of the bag. The transform also imposes a categorical collapse
of elements in the bag into a partition [3]
of the bag’s elements. These upward
movements are abstracted as formal constructions that create a specific
ordering to a specific set of elements. These elements are then laid down into
a new framework aspect set, following the principles of categoricalAbstraction
(Prueitt, 2001).
By making this cross-scale transformation, a
measurement of the elements is occurring.
The measurement is part of both the down and up movements of the cross
scale transform. The scholars have not
settled intellectual problems with a linguistic description of the phenomenon
of cross scale measurement. The leading
work on this problem is by Howard Pattee and Peter Kugler.
By taking the cross-scale transform of T x G, Adi
discovered the dimension of the elementary frame types underlying the use and
practice of the Arabic language.
As defined below, let P be the set of elementary
process types:
Adi discovered that the power set of P constitutes
the elements of a dimension of the realization of the four elementary frame
types.
4. First Level
of the Readware Framework--Substructural Ontology
For notational convenience and completeness, we introduce the following operations defined on sets, frames and lists.
Define a
frame as a unity, indicated by "(-)", filled with a list -, so (a
b c) is a frame.
Define list((-)) = - , where "(-)" is a frame, so list((a b c)) = a b c.
Define list(X) = list of elements of X, where X is a set, so list({a, b, c}) = a b c.
Define frame(-) = (-), where "-" is a list, so frame(a b c) = (a b c).
Define set(-) = {elements of the list - }, so set(a b c) = {a, b, c}.
Let F = { f(i) | i = 1 to 4 } be the set of elementary frame types. For
convenience we may write f1 for f(1), f2 for f(2), f3 for f(3) and f4 for
f(4). We have
f1 = (closed)
f2 = (open)
f3 = (engaged)
f4 = (separate)
Let
P = { p(i) | i = 1, 2, 3 } =
{assignment, manifestation, containment}
be the set of elementary
process types. For convenience we
may write p1 for p(1), p2 for p(2) and p3 for p(3).
We enumerate the power set of P
P* = {s(i) | i = 1 to 8}
{ nul set, {p1}, {p2}, {p3},
{p1, p2}, {p1, p3}, {p2, p3}, {p1, p2, p3} }
Remember that size(P*) = 8.
We now define the "puts" operator on F x P*
puts(s(i), f(j)) = frame( list( set( list( f(j) ) ) union s(i) ) )
which "puts" up to three elementary
process types in one elementary frame type.
We call the resulting frame a substructural
ontological frame type.
The ontology-generating
function B is defined from F x P* to the 4x8 matrix Q
Q = [ q(i, j) | i = 1 to 4
and j = 1 to 8 ]
where
q(i, j) = puts(s(i), f(j))
|
|
(closed) |
(open) |
(engaged) |
(separate) |
|
|
|
(closed assignment) |
(open assignment) |
(engaged assignment) |
(separate assignment) |
|
|
Q = [ |
(closed manifestation) |
(open manifestation) |
(engaged manifestation) |
(separate manifestation) |
] |
|
|
(closed containment) |
(open containment) |
(engaged containment) |
(separate containment) |
|
|
|
(closed assignment manifestation) |
(open assignment manifestation) |
(engaged assignment manifestation) |
(separate assignment manifestation) |
|
|
|
(closed assignment
containment) |
(open assignment containment) |
(engaged assignment containment) |
(separate assignment containment) |
|
|
|
(closed manifestation containment) |
(open manifestation containment) |
(engaged manifestation containment) |
(separate manifestation containment) |
|
|
|
(closed assignment manifestation containment) |
(open assignment manifestation containment) |
(engaged assignment manifestation containment) |
(separate assignment manifestation containment) |
|
Based in intuitive notions, the substructural ontology Q appears to contain all possible
substructural ontological frame types.
A sense of completeness appears to exist. As required, each of the 32 elements of Q has an independent status, and each appears to have a legitimate
basis for being included.
Some issues remain, and these suggest some additional dimension(s) may be required. For example, the notion of duration separates into a descriptive enumeration of a dimension having two elements, static and dynamic. One can see, however, that some nuance exists. We will later discuss the static view of process types as object types.
Conjecture on correspondence between Q and A: We find that we can arrange the 4 vowels and 28 consonants of the
Arabic language in a certain order in a 4x8 matrix A
A = [ a(i, j) | i = 1 to 8
and j = 1 to 4 ]
|
|
vowel_i |
vowel_a |
vowel_u |
sukoon |
|
|
|
ya |
hamza |
waw |
ha |
|
|
A = [ |
meem |
fa |
dal |
thal |
] |
|
|
'ain |
noon |
qaf |
ghain |
|
|
|
ra |
lam |
ba |
ta |
|
|
|
seen |
zay |
ssad |
tha |
|
|
|
kaf |
ddad |
tta |
kha |
|
|
|
hha |
sheen |
geem |
zza |
|
There is a one-to-one ontological correspondence
between the vowels and consonants of the Arabic language and the frame types of
our substructural ontology.
We make the conjecture that an ontological correspondence exists between A and Q. This conjecture will be pursued
objectively. We will require of
ourselves both community consensus and evidence based experimentation with
Arabic text.
[1] http://www.ontologystream.com/beads/enumeration/gFfoundations.htm
[2] A bag is like a set except duplicates are not collapsed into a single element, i.e. the bag [ 3,3 ] has size 2. The set {2,2} has size 1. The elements of the bag have no categorical collapses, nor any notion of order.
[3] In this case the categories each have only one member, but in other cases the formation of categories will organize the lower set in a cross scale transform into a small number of categories. Example, physical chemistry uses only 98 atomic elements.