Saturday, October 16, 2004
Algorithm development using Orbs
Comment from the
Founding Committee
The Adi letter semantics has a three-decade-old development
period and is associated with a 1986 patent on organizing data by collapsing
categories into representations using a single letter.
(See previous note from Tom Adi at [62])
(additional extended
comments by Prueitt [66])
The Readware Framework of Knowledge
By Tom Adi, October 14, 2004
Footnotes by Founding Committee
1. Background
In 1983, I set out to find a theory of language, not an ontology, for a project in machine translation. I did not study linguistics, psychology, modern physics or math. I just loved languages and spoke eight of them.
Being an Arab, I looked at an old Arabic book and asked a single question thousands of times: "What does the context in which a word is used tell me about the relationship between letters and physical reality?"
In Arabic, there is one-to-one correspondence between letters and sounds. Arabic has 28 letters and four short vowels. Most Arabic word roots are tri-consonant, meaning that the root has no vowels, has three consonants.
First, I looked at every contextual usage of single-letter prepositions and other single-letter syntactical units. Then I studied word roots that had a single consonant. Vowels seemed to add less constraint than did consonants. Then I studied two-consonant roots. Finally, I examined certain three-consonant roots.
2. Formal Results
Let S be the set of elementary essences S = {element, domain, order}
P the set of elementary polarities P = {closed, open}
G is the set of elementary engagements G = {self, engaged}
V the set of elementary views V = {object, process}
F is the set of elementary functions F = {operand, relator}
Then E is the set of elementary components E = (S x P x G x V)* x F
and C is the set of useful compounds C is a subset of E 3
Let A be the set of all Arabic letters and short vowels (uppercase letters stand for foreign-sounding Arabic letters):
A = {y, A, w, h, m, f, d, V, O, n, Q, G, r, l, b, t, s, z, C, F,
k, D, T, X, H, S, g, Z, i, a, u, silence}
The size of this set is 32.
Every alphabet A' is a subset of A in some sense.
There is a one-to-one correspondence (partially revealed in the Readware Orb)
A <=> S* x P x G
and a one-to-many categorical collapse correspondence [1]
A => E
The dual of the categorical collapse correspondence is a many-to-one correspondence (interpretation). We use the set N to indicate the set of interpretations:
N is a subset of A 3 <=> subset of C. (need to clarify the use of <=> )
Based on context rules, a tri-consonant <a, b, c> out of A 3 has one of the structures
<a, r, b>, <r, b, c>, <a, b, r>
where r means that the letter in that position has the elementary function of relator while the other two letters are operands.
A tri-consonant may also have two cooperating relators r1 and r2:
<r1, r2, c>, <r1, b, r2 >, <a, r1, r2>
These cooperating relators play an allosteric, meaning “indirect but essential”, role in the possible collapses and interpretations of the categories. At this time we have only two “non-specific” allosteric relators, and no type of type that creates a clear understanding of the allosteric relators. We suggest that the role that these relators have is functional both in the one-to-many expression and the many-to-one collapse into categories.
The many possible interpretations of the notational convenience
< a, b, c >
are constrained by a specific “pragmatic” structure and by the contextualization that is occurring for the specific a, b, or c.
Emergence is when an interpretation is chosen because it seems to somehow fit at the moment. "Ultimate reality" is cloaked. Given a specific < a, b, b >, other interpretations, or expressions, are always possible. However specific tri-consonant, bi-consonant and uni-consonant word roots do constrain our interpretation process due to the mechanisms involved in cognition.
3. "Emergent"
Relationships Between
the Readware Framework and the Sowa-Ballard Framework
Sowa-Ballard’s "continuant" and "occurrent" bear a resemblance to Readware’s elementary views "object" and "process." Sowa-Ballard’s "independent" and "relative" may correspond to Readware’s "self" and "engaged."
Sowa-Ballard’s framework sees "physical" as an interpretation of "abstract."
Readware’s framework sees "mediating" and "universal" implicitly corresponding to the structures of word roots.
The Challenge Problem implies a process in which the relationship between Sowa-Ballard’s frameworks and the Readware framework can be objectively examined.
4. Readware’s categoricalAbstraction (cA) and eventChemistry (eC)
The proposed integration of Readware framework and the Orb construction makes use of Readware notational conventions. The Orb structural encoding into computer memory allows many types of traditional data mining algorithms to be almost instantly applied to Readware information.
Once we make this technical integration, one is able to apply the cA and eC principles from stratification theory, developed by Prueitt (1995 – 2002).
Two views of structural data are enforced:
· The object view of elementary essences is called particle and here we use the names of a set of proposed elementary essences.
·
The process view of elementary essences is called eventicle (assignment, manifestation,
containment).
This means, for example, that the process view of order is containment. More on the Readware collapse and express methodology has to be developed as part of the Challenge Problem. A few observations can be made now.
1) Polarities are crossed with elementary engagements and combined with eventicles and particles.
2) Eventicle polarities are backward (self, closed), forward (self, open), joining (engaged, closed) and takingApart (engaged, open).
3) Particle polarities are called states and their names are derived in a similar way (closed, open, together, apart).
A slightly different set of observations are:
1) Atom is the object view of a letter.
2) ElementaryEvent is the process view of a letter.
3) Concepts are word roots (tri-consonant, bi-consonant, and uni-consonant).
4) A relator letter is an ElementaryEvent that is "acting upon" one or more Atoms.
Some concluding observations are
1) Concept interpretations can be expressed in different ways, but they must describe an element of C.
2) Some interpretation expressions are attached to concepts as expressed in the Orb notation [2].
[1] This many-to-one correspondence involved tow types of category collapses. All elements of E that correspond to the same element of A forms a category, or equivalence class. The equivalence class has the property that all elements in the class are treated without distinguishing any differences between any other element of that class. The one that corresponds to the many is deemed a category representative. How the collapse of category occurs in real world human use of language is an issue to be explored in the Challenge Problem. How a category unfolds into a specific use of language, as a part of a word or as part of a phrase or passage is a one-to-many entanglement in real time within a pragmatic context. This is also a open question as to how this occurs both as an aspect of individual thought and generation of words in sentences, and as heard/read and interpreted by members of the community sharing that language in common.