The Construction of Words

This page is about the regular construction of words from a syntactic point of view. Explanations about the meaning of the primitive symbols and the IEML alphabet can be found in this page (the six primitives) and this one (the 25 lower-case letters)

IEML contains about 3,000 words forming the basic semantic building blocks, or elementary concepts, from which all the expressions of the language are composed. The words are generated regularly from six primitive symbols which form the layer 0 of the language. The generative operation being recursive, the words are stratified on six layers above the layer 0.

The primitive symbols are: E (emptiness), U (virtual), A (actual), S (sign), B (being), and T (thing).

The meanings of the words are not attributed by some arbitrary translations into another language, but is defined through a network of explicit semantic relations inside the IEML dictionary.

, by using emptiness elision processes at the end of the expression and by representing certain chains of three primitives by a lowercase letter.

The morphological function

The words are generated recursively by a three-role non-commutative multiplicative operation that concatenates the words of the lower layer.

The three syntactic roles of the ternary concatenation are : 

the substance (role 1), the attribute (role 2) and the mode (role 3) 

Only words of the same layer can be multiplied.

Thus, a word is a ternary concatenation (recursive on 6 layers) of primitive symbols.

At layer one we have words of the form: « U:S:E:.   U:B:E:.   U:T:E:.   A:S:E:.   A:B:E:.   S:T:E:. » etc. Words are generated by operations of the form, « U:⊗S:⊗E: = U:S:E:. »

At layer two we have words of the form: « U:S:E:.U:B:E:.U:T:E:.- A:S:E:.A:B:E:.S:T:E:.-« , etc.  Words are generated by operations of the form: « U:S:E:. ⊗ U:B:E:. ⊗ U:T:E:. = U:S:E:.U:B:E:.U:T:E:.- « 

We stop at the sixth layer, which is more than enough to generate a dictionary of 3000 words. Punctuation marks ( : . – ‘ , _ ; ) are used to identify the successive layers, from layer 0 (:) to layer 6 (;) . In homage to Spinoza, the three roles of the morphological operation are called substance (the first place), attribute (the second place) and mode (the third place).

There is an additive operation, which is a simple union of sequences of the same layer. The additive operation is commutative, but the order of the letters is normalized to ensure that no two formally different expressions have the same meaning.

Multiplication is distributive over addition. For example, « U: ⊗ (S: ⊕ B: ⊕T:) ⊗ E: = U:S:E:. ⊕ U:B:E:. ⊕ U:T:E:. »

On a mathematical level, the algebra resulting from the 6-symbol alphabet, the non-commutative ternary multiplication and the addition has a non-commutative ring structure[1]. Note that the word ring, defined by an alphabet and two operations, includes in principle an immense number of variables, but only three thousand of them have a lexical meaning. The number of words is kept « small » to facilitate both automatic semantic computation and cognitive management of the language for humans.

Note: [1] See the demonstration on a 2015 version of IEML: in particular chapter 5. About non-commutative algebra, note the work of Alain Connes Non-Commutative Geometry. Paris: InterEditions, Academic Press, Boston MA, 1994 .

In practice, the words appear as sequences of letters of a 35-character alphabet (10 capitals and 25 lowercase letters) interspersed with punctuation marks without spaces. The final punctuation mark of a word indicates the syntactic layer of the word, while the internal punctuation marks are traces of the recursive concatenations of which the word is the product. The meaning of the letters (below) is only indicative: each letter essentially designates a place in a system of symmetry.

10 capital letters 

  • E = emptiness
  • U = virtual
  • A = actual
  • S = sign
  • B = being
  • T = thing

Learn more about the semantic primitives.

  • Virtual/actual binary symmetry
    • O = U⊕A = process 
  • Ternary symmetry sign/interpreter/referent
    • M = S ⊕B⊕T = entity or representation, 
  • 2/3 symmetry: process/entity
    • F = O⊕M = fullness
  • 5/1 Symmetry fullness/emptiness
    • I = F⊕E = information

25 lowercase letters

In the ternary concatenations represented below, the final E is elided. For instance U:U:E:. becomes U:U:.

Table 1: the 25 lower case letters

The above table shows an example of an IEML paradigm at layer 1, that of the lower case letters. In Table 1, codes with punctuation marks are IEML expressions, and their English translation is shown below. IEML codes have two components, selected from the semantic primitives U: (virtual), A: ( actual), S: (sign), B: (being), and T: (thing). The first component corresponds to the syntactic role « substance » and the second to the syntactic role « attribute ». Codes with the same substance are on the same row, and codes with the same attribute are on the same column. The punctuation mark  » :  » means « layer 0″ and the punctuation mark  » .  » means « layer 1 ». In order to reduce space and complexity, the pairs (substance, attribute) of the primitives (U: A: S: B: T:) are represented by 25 lowercase letters. For example, T:T:. is represented by « l ».

The meaning of the 25 lower-case letters is explained further here.

Punctuation marks

  • Layer 0 :
  • Layer 1 .
  • Layer 2
  • Layer 3
  • Layer 4 ,
  • Layer 5 _
  • Layer 6 ;

k.i.- means « gift » because gifts weave the social bond (k. in substance) through a material « doing » (i. in attribute). The emptiness in mode is elided.

k.i.-k.i-‘ means « economic good » by suggesting a relationship between the increasing complexity of the exchange of gifts and counter-gifts and the development of the economy. Here the gift k.i.- is repeated in substance and in attribute, and the emptiness E: in mode is elided.

Example of a Paradigm at layer 2

Table 2: Human Development Paradigm

In the Table 2 above, the 54 IEML expressions in the matrix cells have two lowercase characters, the first corresponding to the syntactic role « substance » and the second corresponding to the syntactic role « attribute ». These characters are chosen from the upper right (yellow) and lower right (blue) quadrants of Table 1: « 25 lowercase letters ».

The table is called « human development » as it declines the kinds of knowledge, values, skills, signs, social roles and techniques (columns) according to the nine interdependent dimensions of human experience: reflection, language, memory, society, emotion, world, truth, life and space (rows).

Again, expressions with the same substance are in the same row and expressions with the same attribute are all in the same column. The punctuation mark « – » means « third layer ». The reader can easily see that a row or a column contains concepts that have some meaning in common, and that the common semantic feature is represented in IEML by the same character.

Learn more about IEML paradigms.

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