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.