Part III

 

The Adi Ontology

Part II:  Functional Ontology

By Tom Adi, November 23, 2004

Version 23

 

In Part I, we introduced our first layer of abstraction, a complex abstract framework called the substructural ontology.  The substructural framework operator q generates the 8x4 matrix Q whose elements are each a substructural frame.  Adi derived q by induction from notions associated with the contextual usage of the elements of the 8x4 matrix A of Arabic vowels and consonants.  We conjecture that Q is an abstract representation of all elementary processes in the real world.

 

In Part II, we will derive our second layer of abstraction from notions associated with the contextual usage of Arabic word stems.  These notions indicate that stems represent function frames, a higher order framework which we conjecture to be the ontology of real-world functions that consist of elementary processes.

 

 


1. Review of Substructural Ontology

 

The substructural ontology is a complex abstract framework defined by the operator q that generates the 8x4 matrix Q. The cells of Q are substructural frames that each have three components

 

1) a substructural polarity consisting of a substructural boundary aspect and a substructural engagement aspect

 

2) up to three substructural processes from the set {assignment, manifestation, containment}. If the substructural frame contains more than one process, then the substructural precedence operator C determines that one process has precedence over the others and will act upon them.  Assignment has substructural precedence over manifestation and containment.  Manifestation has substructural precedence over containment.

 

3) a discretionary ontological operater V that allows the ontology user to obtain a static view of any substructural process.

 

The key substructural abstract aspects are: polarity (boundary and engagement), processes (central aspect) that may act upon each other as determined by the substructural precedence operator C, and the discretionary static view of a process (object).

 

The static view operator V is simply a measurement device that comes with each substructural "package."  It allows the observer (ontology user) to have a snapshot or a freeze frame of any substructural process.

 

A substructural frame is a process with polarity that may act upon other processes over which it has substructural precedence.

 

None of the four substructural frames in the first row of Q has any processes.

 

The next three rows have one process per frame.  The frames in row two have the process assignment, in row three the manifestation process, and in row four the containment process. The following three rows, five, six and seven have two processes. In row five assignment acts on manifestation, in row six assignment acts on containment, in row seven manifestation acts on containment.  Each of the four substructural frames in the last row has assignment acting on manifestation and containment.

 

The 8x4 matrix A of Arabic vowels and consonants is a representation of Q.

 

The first row of A--which represents the first row of Q--consists of the Arabic vowels.  The rest of A consists of consonants.

 

In other words, vowels represent substructural frames without processes. Consonants represent substructural frames with processes.

 

In Arabic, vowels are mostly not written.  They are not considered letters.  But along with certain added consonants, vowels play an important role in creating thousands of word forms out of each stem.  Word forms express different aspects of the stem such as time of action and verb conjugations, place of action, actor, duals, plurals, adjectives, manner of action, frequency, quality, instrument and so on.

 


2. Notions Observed in Contextual Usage of Arabic Word Stems Indicate Inheritance and Extension of the Properties of the Substructural Ontology 

 

Adi observed notions in the contextual usage of Arabic vowels and consonants which indicate abstract aspects that make up the complex framework called substructural ontology.

 

Of particular importance are the substructural frames represented by consonants from the fifth to eighth rows of A.  Each of these frames contains two or three processes, and the substructural precedence operator C grants one of them substructural precedence, i.e. the power to act upon the other process(es).  For example, the assignment process always has the power to act upon the other processes (manifestation and containment).

 

An Arabic word stem is a string of three consonants.  Remember that each consonant represents a substructural frame that contains one or more processes.  A stem then represents a combination of substructural frames that contain processes.  Adi wanted to know whether the notions observed in the contextual usage of a stem indicate the existence of a higher order precedence operator, say C2, that grants to some of these substructural frames the power to act upon the other substructural frames.

 

Adi studied the notions found in the contextual usage of all occurrences of over a thousand verb stems in an old Arabic book. He selected these stems as the simplest in meaning from a total of around seventeen hundred and fifty stems that the book uses. Let's call this set of observed notions N3. The size of N3 is estimated at about ten thousand observed notions.

 

Adi found that the observed notions N3 do indeed indicate with great regularity that the substructural frames represented by the consonants in a stem do act upon each other to fulfil some function. We therefore call the combination of substructural frames that is represented by a stem a function frame.

 

Inside a substructural frame, the assignment process has substructural precedence over manifestation and containment, and manifestation has precedence over containment.  This is all there is to the substructural precedence operator C.

 

In a function frame, we have up to three substructural processes per substructural frame and we need to determine which substructural frame has functional precedence.

 

N3 indicates that substructural frames which contain the assignment process (the first, fifth, sixth and eight rows of Q) have precedence over substructural frames that do not contain assignment (third, fourth and seventh rows of Q). N3 actually indicates that substructural frames with processes that have substructural precedence (for example, assignment) also have functional precedence over substructural frames that contain processes with lesser substructural precedence (for example, containment).  We speak here of the functional inheritance of substructural precedence.

 

N3 also indicates that substructural frames which contain fewer processes have precedence over those with more processes.  We call this the functional precedence of simplicity:  the least complex substructural frames have functional precedence.

 

These indications from the observed notions N3 are the basis of the functional precedence operator C2.

 

Define the inherited substructural process precedence factor K as follows

 

K(assignment) = 100

K(manifestation) = 10

K(containment) = 1

 

The functional precedence operator C2 calculates a functional precedence factor for each row of the substructural ontology Q as follows

 

C2 (i) = (6 * Sum ( K(p(n) ) ) | p(n) is in s(i) )  / size(s(i))

 

where i = 1 to 8

p(n) is a substructural process out of subset s(i)

s(i) is a member of the enumerated power set P*

the multiplier 6 secures integer functional precedence factors

 

We have

C2 (1) = 0 

C2 (2) = 6*100 / 1 = 600 

C2 (3) = 6*10 / 1 = 60

C2 (4) = 6*1 / 1 = 6

C2 (5) = 6*110 / 2 = 330

C 2 (6) = 6*101 / 2 = 303

C2 (7) = 6*11 / 2 = 33

C2 (8) = 6*111 / 3 = 222

 

A substructural frame has functional precedence if it belong to a row with a higher functional precedence factor.  Thus we have a descending precedence sequence of the rows of Q

 

2, 5, 6, 8, 3, 7, 4, 1

 

In a function frame, if one substructural frame has functional precedence over the other two substructural frames, then it is called the controller.  The controller runs an interaction between the two other substructural frames, the controlled frames. The substructural process(es) of the controller dictate(s) an interaction theme.  We have a thematic interaction frame.

 

If the controller is from the second row of Q, then we say we have an interaction by assignment.  If the controller is from the fifth row of Q, then we have an interaction by assignment of manifestation.  And so on.

 

"Process A acts upon process B" was first inherited from the substructure and then extended to "process A causes another process B to act upon a third process C."

 

The polarity of the controller in a thematic interaction frame determines interaction polarity, i.e. the direction in which the controlled substructural frames act upon each other

 

"inward" means "controller makes right frame act inward upon left frame"

"outward" means "controller makes left frame act outward upon right frame"

"engaged" means "controlled frames are joined by the controller"

"separate" means "controlled frames are separated by the controller"

 

Thematic interaction frames inherit interaction polarity from substructural polarity and extend it to create a special control structure, a special type of function.

 

We will now demonstrate thematic interaction frames. Controllers are in italics.  Consonant names and associated notions from N3 are in parentheses.

 

Remember that the 8x4 matrix A of Arabic vowels and consonants corresponds to the 8x4 matrix Q of substructural frames.

 

Frames of Interaction by Assignment.  If we have a thematic interaction frame and the controller is a substructural frame from the second row of Q, then we have a frame of interaction by assignment.  The controlled frames are simply assigned to manifest themselves upon each other according to interaction polarity. There is a single soft consonant (ya, hamza, waw, ha) in the corresponding stem and the notions associated with such stems indicate interaction by assignment.

 

"ya ta meem" (orphan):  inward manifestation (meem, a person) is assigned inward to separate manifestation assignment (ta, not belonging).

 

"hamza fa qaf" (horizon):  outward manifestation (fa, appearance) is assigned outward to engaged containment (qaf, meeting of spheres).

 

"waw qaf fa" (arrest):  assignment to join engaged containment (qaf, confinement) and outward manifestation (fa, someone free).

 

"ha dal noon" (cease fire):  assignment to separate engaged manifestation (dal, confrontation) and outward containment (noon, violation or unleashed force).

 

"fa ha meem" (understand):  assignment to separate outward manifestation (fa, the undefined) from inward manifestation (meem, the defined).

 

 

Frames of Interaction by Allocation.  If we have a thematic interaction frame and the controller is a substructural frame from the fifth row of Q, then we have a frame of interaction by assignment of manifestion or interaction by allocation for short.  The controlled substructural frames are allocated to each other according to interaction polarity. There are no soft consonants (ya, hamza, waw, ha) in a stem, but there is a single consonant from the fifth row of A (ra, lam, ba, ta).  Notions associated with such stems indicate interaction by allocation.

 

"thal kaf ra" (remember):  inward containment of manifestation (kaf, storage event) is allocated inward to separate manifestation (thal, specific event).

 

"fa kaf ra" (think):  inward containment of manifestation (kaf, storage event) is allocated inward to outward manifestation (fa, undefined event).

 

"'ain lam meem" (know):  inward containment ('ain, defined order) is allocated outward to inward manifestation (meem, defined phenomenon).

 

"noon ba thal" (cast away): allocation to join outward containment (noon, bringing out) and separate manifestation (thal, keeping separate).

 

"fa ta qaf" (unravel, creation of cosmos):  allocation to separate outward manifestation (fa) and engaged containment (qaf, seam or bond).

 

Frames of Interaction by Assignment of Containment.  If we have a thematic interaction frame and the controller is a frame from the sixth row of Q, then we have a frame of interaction by assignment of containment. The controlled substructural frames interact by assigned containment according to interaction polarity.  There are no soft consonants (ya, hamza, waw, ha) in the stem and no consonants from the fifth row of A (ra, lam, ba, ta), but there is a single consonant from the sixth row of A (seen, zay, ssad, tha).  Notions associated with such stems indicate interaction by containment.

 

"fa seen dal" (disrupt, destroy):  assignment of containment (seen, change of structure) of engaged manifestation (dal, whole thing) inward (a reduction) to outward manifestation (fa, damage).

 

"'ain zay meem" (resolve):  assignment of containment (zay, assignment of energy) of inward containment ('ain, personal strength) outward to inward manifestation (meem, personal action).

 

"ssad 'ain qaf" (thunderbolt, knock out):  inward containment ('ain, force) is joined by assignment of containment with (discharged at) engaged containment (qaf, force interface).

 

"ssad dal qaf" (truthfulness):  engaged manifestation (dal, what really happens) is joined by assignment of containment (matched by measurement) to engaged containment (qaf, shared perception).

 

"tha meem noon" (price):  inward manifestation (meem, defined thing) is separated by assignment of containment (a number) from outward containment (noon, undefined order).

 

 

 

Frames of Interaction by Processing.  If we have a thematic interaction frame and the controller is from the eighth row of Q, then we have a frame of interaction by assignment of manifestion and containment or interaction by processing for short. The controlled substructural frames are processed (a generic term for doing whatever it takes) according to interaction polarity. There are no soft consonants (ya, hamza, waw, ha) in the stem, and no consonants from the fifth row of A (ra, lam, ba, ta), and no consonant from the sixth row (seen, zay, ssad, tha), but there is a single consonant from the eighth row (hha, sheen, geem, zza).  Notions associated with such stems indicate interaction by some generic processing or a complex control process.

 

"'geem meem 'ain" (gather):  process to join inward manifestation (meem, defined persons or objects) and inward containment ('ain). 

 

"'geem meem dal" (solid):  process to join inward manifestation (meem) and engaged manifestation (dal).

 

"'hha meem dal" (credit, praise):  processing of engaged manifestation (dal, attribution, causality) inward to inward manifestation (meem, person).

 

"'sheen fa qaf" (twilight):  processing of outward manifestation (fa, appearance) outward to engaged containment (qaf, meeting of spheres).

 

"'zza 'ain noon" (cabin of vehicle):  process to separate inward containment ('ain) and outward containment (noon).

 

 

If two of the three substructural frames in a function frame belong to the same row of Q--and thus have equal functional precedence factors--then we have a new kind of function.

 

If in a function frame two substructural frames share a functional precedence factor that is higher than that of the third substructural frame, then we have two controllers and a single controlled substructural frame.  The controllers perform a control procedure upon the third substructural frame.

 

Procedural Control Frames.  If a consonant repeats or there are two consonants from the same row in a stem, and the third consonant represents a substructural frame with a lower functional precedence factor, then the observed notions indicate that both consonants perform a procedure on the third.  Different control procedure types are created by different controller polarity pairs.  Each control procedure type can be used to achieve a variety of control tasks.  A inward-outward controller pair is an inward-outward control procedure.  An engaged-separate pair is a joiner-separator control procedure.  A inward-engaged pair is a retro-joiner control procedure.  A inward-separate pair is a retro-separator control procedure. An outward-engaged pair is an outward-joiner control procedure.  An outward-separate pair is an outward-separator control procedure.  The duplicate polarity pairs (inward-inward etc.) are simply called inward control procedure, outward control procedure, joiner control procedure, and separator control procedure.

 

"kaf ta ba" (write, prescribe): join-and-separate allocation procedure (ta ba, create allocations and de-allocations) on inward containment manifestation (kaf, storage event or law application).

 

"qaf ta lam" (kill): outward-separator allocation procedure (ta lam, break and leave broken) applied to engaged containment (qaf, connected force, life).

 

"kaf ba ra" (big): retro-joiner allocation procedure (ba ra, adding up) applied to inward containment manifestation (kaf, size)

 

"ra ta qaf" (sewed up, cosmos before creation): retro-separator allocation procedure (ra ta, removing to the very last) on engaged containment (qaf, flaps, engaged forces).

 

"ddad lam lam" (stray): outward allocation procedure (lam lam, open ended) on outward containment of manifestation (ddad, disorderly action).

 

 

Function Frames With Only Two Elements. In three consonant stems where the soft consonant "ya" or "waw" occupies the second or third position, this consonant is often considered a stretched vowel (vowel_i, vowel_a, or vowel_u).  The stems are thus reduced to two-consonant stems.  Vowels represent substructural frames without processes.

 

We then have a function frame with only two substructural frames.  Two substructural frames have a simple control relationship.  The one with a higher functional precedence factor controls the other.  If the functional precedence factors are equal (same row of Q), then the two substructural frames collaborate and perform like a control procedure.

 

"noon waw ra" (fire, light, waw is seen as stretched vowel_a or stretched vowel_u): inward allocation (ra) on outward containment (noon, free energy).

 

"qaf waw lam" (say, waw is seen as stretched vowel_a or stretched vowel_u): outward allocation (lam, addressing) on engaged containment (qaf, speech).

 

"noon seen ya" (forget, ya is seen as stretched vowel_i): inward assignment of containment (seen, lock) on outward containment (noon, retrieval).

 

"fa dal ya" (compensation, ya is seen as stretched vowel_a): outward joiner of manifestation (fa dal, spend something to match something).

 

"tta ghain ya" (transgress, ya is seen as stretched vowel_a): engaged containment of manifestation on (tta, grab) separate containment (ghain, owned by others).

 

"ghain tta ya" (cover, ya is seen as stretched vowel_a): engaged containment of manifestation (tta, apply containment) on separate containment (ghain, uncontained).

 


3. Second Layer of Abstraction--Functional Ontology

 

While a substructural frame contains up to three substructural processes, a function frame consists of two or three process-containing substructural frames.  It is an element of QP2 or QP3 where QP is the matrix consisting of the second to eighth rows of the 8x4 matrix Q. These rows correspond to the consonant rows of the matrix A of Arabic vowels and consonants.

 

There are 282 + 283 (22,736) potential word stems, but the largest Arabic dictionaries only have a total of around 4,000 stems.

 

The functional precedence operator C2 calculates the functional precedence factor for all the substructural frames that make up a function frame.  The substructural frames with higher factors are called controllers.  Controllers excercise control over the other substructural frames in the function frame.  This means acting upon other substructural frames or causing substructural frames to act upon each other using the substructural processes and polarities of the controllers.

 

Single-controller functions are called thematic interaction frames.  Dual controller functions are called procedural control frames.

 

Our second layer of abstraction consists of function frames that act according to functional precedence rules based on two principles: inheritance of substructural precedence and dominance of simplicity.  We call this layer the functional ontology.  It is derived from notions observed in the contextual usage of Arabic word stems.

 

We conjecture that each function frame is an ontological representation of an individual real-world function, system or subsystem.

 

In Part III, we will look at our cognitive ontology layer where function frames are implemented in real-world environments.