The Readware Framework for Knowledge Processing--Part I


By Tom Adi, October 23, 2004



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:


P = {assignment, manifestation, containment}


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)




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 ]




q(i, j) = puts(s(i), f(j))











(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)



















 assignment 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 ]















A = [





































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. 




[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.