Adi’s Semantic Theory

Parts I and II of the Adi Theory of Semantics state that each Arabic vowel and each consonant is a sign that refers to a pair of compound abstract objects: a process and a polarity. They also state that the 28 consonants and four vowels of Arabic are organized in a 4×8 matrix that represents the relationships of symmetry among the corresponding abstract objects (Adi, 2007).

Part I (Polarities). There is a set T = {closed, open} containing two abstract objects representing symmetrical boundary conditions, and there is a set G = {self, others} containing two abstract objects representing symmetrical engagement conditions, such that the product of the two symmetry sets, supersymmetry set R, i.e.,

R = T x G = { r(j) | j = 1 to 4 }

= { (closed, self), (open, self), (closed, others), (open, others) }

or using a shorthand notation

= {inward, outward, engaged, unengaged}

is a set of abstract object pairs that represent polarities.

If we arrange all Arabic sounds as follows in the 4 x 8 matrix

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	tha	]
	‘ain	noon	qaf	ghain
	ra	lam	ba	ta
	seen	zay	ssad	tha
	kaf	ddad	tta	kha
	hha	sheen	geem	zza

then all the sounds a(i, j) of column j, will have elements of meaning that interpret polarity r(j) and no other polarity.

Part II (Elementary Processes & Elementary Control Precedence). There is a set of abstract objects that we shall call elementary processes

P = { p(i) | i = 1, 2, 3 } = {assignment, manifestation, containment}.

For convenience, we write pi for p(i) and enumerate the power set of P

P* = {s(i)| i = 1 to 8}
= { {},{p1}, {p2}, {p3}, {p1, p2}, {p1, p3}, {p2, p3}, {p1, p2, p3} }

When a set s(i) contains more than one elementary process, then we have an elementary process combination. To simplify, we will refer to each set s(i) as a process.

All the sounds a(i, j) of row i of A have elements of meaning that interpret process s(i) such that if there is more than one elementary process in s(i), then the elementary process pk with lowest row number k is applied to, or controls, the remaining elementary processes. We say that p1 has elementary control precedence over p2 and p3, and p2 has control precedence over p3.

The first two parts of the theory are visualized in Table 1. Tables 2 and 3 list prominent interpretations of polarities and processes, respectively.

Table 1. Abstract objects of Old Arabic sounds

ELEMENTARY	P O L A R I T Y
P R O C E S S	inward	outward	engaged	unengaged
1. no process	vowel_i	vowel_a	vowel_u	sukoon
2. assignment	ya	hamza	waw	ha
3. manifestation	meem	fa	dal	thal
4. containment	‘ain	noon	qaf	ghain
5. = 2 on 3 allocation	ra	lam	ba	ta
6. = 2 on 4 ordering	seen	zay	ssad	tha
7. = 3 on 4 mapping	kaf	ddad	tta	kha
8. = 2 on 3 & 4 generic process	hha	sheen	geem	zza

Table 2. Prominent interpretations of polarities

inward (closed, self)	outward (open, self)	engaged (closed, others)	unengaged (open, others)
backward connect to self defined enclosed one’s own recursive repeat self-contained	empty-self expand free invalid open to others undefined	common general join shared together	cut disengage exchange separate special specify

Table 3. Prominent interpretations of processes

2. assignment	element, identify
3. manifestation	activity, event, method, person, place, space, time
4. containment	command, control, energy, force, instruction, order, speech, value
5. allocation (assignment of manifestation)	apply, belong, link, a set
6. ordering (assignment of containment)	lodging, measure, structure
7. mapping (manifestation of containment)
8. generic process (assignment of manifestation and containment)	behavior, motion, object, processing, thing

We also created Table 1 for the sounds of English and for other languages (Adi & Ewell, 1987b, 1987d, 1996). However, we were not able to fill all the cells of the table for any language other than Arabic.

Parts III and IV of the Adi Theory of Semantics establish rules for the interpretation of the abstract structures to which three-consonant Arabic word roots refer. Most Arabic word roots are strings of three consonants each. A few roots consist of four, and even fewer roots consist of five consonants. Each consonant a(i, j) is a sign that refers to one non-empty process s(i) from P* (i = 2 to 8 ) and one polarity r(j) from R (see the Adi Theory of Semantics, Parts I & II and Table 3). Thus, a three-consonant root is a structured sign.

Root “a(i, j) a(k, m) a(n, q)” refers to three process-polarity pairs

(s(i), r(j)), (s(k), r(m)), (s(n), r(q))

where i, k, n = 2 to 8 are the rows of A, corresponding to the processes

s(2) = assignment, s(3) = manifestation, s(4) = containment

s(5) = assignment of manifestation, shorthand = allocation

s(6) = assignment of containment, shorthand = ordering

s(7) = manifestation of containment, shorthand = mapping

s(8) = assignment of manifestation & containment, shorthand = generic process

and j, m, q = 1 to 4 are the columns of A , corresponding to the polarities

r(1) = (closed, self), shorthand = inward

r(2) = (open, self), shorthand = outward

r(3) = (closed, others), shorthand = engaged

r(4) = (open, others), shorthand = unengaged

Part III (Control Precedence among Process-Polarity Pairs). Based on observations on the relationships suggested by context between the elements of meaning represented by some word roots, we define the inherited elementary control precedence factor K (see Theory Part II) such that K(assignment)=100, K(manifestation)=10, and K(containment)=1 and then use K to calculate the process-polarity pair control precedence factor C for any process-polarity pair ((s(i), r(j)) as follows

C ( (s(i), r(j)) ) = (6 * Sum ( K(p(n) ) ) | p(n) is in s(i) ) / size(s(i))

where i = 2 to 8 and s(i) is a process, a member of P*

and j = 1 to 4 and r(j) is a polarity from R

and p(n) is an elementary process from P out of subset s(i)

and the multiplier 6 secures integer functional precedence factors

C (2) = 6*100 / 1 = 600

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

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

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

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

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

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

in order to determine the control precedence relationships needed to interpret sound combinations such as word roots and word forms. We notice that the precedence factor C does not depend on polarity.

Since word root “a(i, j) a(k, m) a(n, q)” is a structured sign that refers to the abstract object structure (a triple of process-polarity pairs)

( ((s(i), r(j)), (s(k), r(m)), (s(n), r(q)) )

then those process-polarity pair(s) which have the highest C value will control (are applied to) the remaining process-polarity pair(s).

C produces a descending control precedence for the rows of A

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

assignment, allocation, ordering, process, manifestation, mapping, containment

For example, assignment controls allocation and ordering controls containment.

Part IV (Types of Root Interpretation Mappings). The interpretation of Arabic word roots is governed by mappings or compositions of mappings whose domains and ranges are infinite sets of interpretations of process-polarity pairs. The mappings themselves also are infinite interpretations of process-polarity pairs. Only the following types of root interpretation mappings are associated with Old Arabic three-consonant roots. The corresponding process-polarity pairs are identified by the subscripts.

1. mapping (one controller)	fij : Xkm ==> Ynq
2. mapping, unspecified range (one controller)	fij ( xkm )
3. composition, unspecified range (two controllers)	fij ( gip ( xkm ) )
4. composition, unspecified domain & range(two controllers)	fij ( gip ( ) )
5. double composition, unspecified domain & range (three controllers)	fij ( gip (hiw ( ) )

where

i, k, n = 2 to 8 is the index of process s() from P* associated with A rows 2 to 8j, m, p, q, w = 1 to 4 is the polarity associated with A columns 1 to 4