IEML Paradigms

Structure of languages

Components: phonemes and words

We know that languages evolve, differentiate and hybridize, but for the purposes of analysis, we will consider the structure of a language at a given moment. A language is built from a few sound units (between thirty and a hundred): phonemes, which have no meaning and are generally divided into consonants and vowels. Some languages also have « click » consonants (in eastern and southern Africa) and others (in Mandarin Chinese) use different tones on their vowels.

Units of meaning – called morphemes – are made up of sequences of phonemes. What most people call words are actually clusters of a few meaning units. For example, the word «tartlets» contains: the concept of «tart», the diminutive «let» and the plural mark «s». It is considered that speakers of a language have a dictionary of between three thousand (minimum proficiency) and thirty thousand (maximum proficiency) lemmas, the latter being canonical words, independent of conjugations, inflections, cases, etc.

Since my goal here is only to give a broad outline of the structure of languages, and although the reality is more complex, I will call « words » the elementary units of meaning and « sentences » their grammatical composition in compound units of meaning.

The syntagmatic axis

According to Roman Jakobson and the structuralist school of linguistics, a language crosses two axes: syntagmatic and paradigmatic. Let’s start by defining a syntagm: it is a sequence of words – a sentence or a phrase – belonging to a language whose grammatical rules allow us to reconstruct the dependency tree and the role of each leaf in this tree. Let’s consider the sentence: « I eat a cake ». The grammatical rules of English tell us that the subject (or first actant) is placed before and the object (or second actant) after the verb. We deduce that the verb to eat is at the root of the tree of which we clearly identify two distinct leaves: the subject (I) and the object (a cake).

Figure 1 The syntagmatic axis: a string of sounds is organized in a dependency tree

The use of conjunctions, punctuation marks – written or spoken – as well as some grammatical rules code the hierarchies of dependencies between main and secondary propositions, between a sentence and its contained phrases, between a phrase and its words. Their place in the phonetic sequence or the use of cases allow us to recognize the grammatical role of words: verb or process, subject or first actant, object or second actant, addressee or third actant, manner complement, etc. 

I can only understand a sentence if, from a sequence of phonemes, on the one hand, and from the knowledge of the dictionary and of the grammatical code specific to my language, on the other hand, I reconstruct a syntactic-semantic nesting scheme whose topological structure is that of a tree. From this tree structure, in which the grammatical role of each word is determined, I infer the scene or mental model that my interlocutor had in mind. Conversely, I pronounce a meaningful sentence when, from a mental model, I first build a syntactic tree of concepts represented by words (a « deep structure » according to Noam Chomsky) which I then transform into a sequence of sounds following the grammatical rules of my language. Of course – except in the case of deliberate literary creation – these different logical steps are taken almost simultaneously and unconsciously.

The paradigmatic axis

The paradigmatic axis is « perpendicular » to the syntagmatic axis. In general, paradigms are groups of substitutions on the nodes of a syntagmatic tree. The best known examples of paradigms are those of conjugations or declensions that we learned in school. 

Let’s consider again the sentence « I am eating a cake ». By keeping the present tense and the grammatical object (second actant), I can vary the person and the number of the subject (or first actant) and substitute to « I », the series: « you, he or she, we, you, they  » while harmonizing the verb. I can also vary the tenses by keeping the mode: “ate” (preterit), « was eating » (imperfect), “will eat » (future). I can also, still for the same sentence, keep the mode, the tense, the grammatical person and the object but replace “eating » with “cooking », “baking », « sharing », etc. In the latter case, I have varied the lemma or, if one prefers, the concept of the action. However, I can’t do it just any way. How could I « debunk » or « tickle » a cake, for example (except in a highly metaphorical sense)?

This means that there is a paradigm of actions – and therefore verbs – that are suitable with the word « cake » in the grammatical object role (or second actant). Similarly, I can eat a cake, a radish or a chicken, but a locomotive, a political constitution or a nightmare would be much less nourishing. There is therefore a paradigm of edible items in grammatical object role that are appropriate with the verb « to eat ».

Figure 2 The paradigmatic axis: each word in a sentence is selected from a matrix of alternative possibilities relevant to the context

A set of words that can be substituted for each other in the same syntagmatic role within a given sentence constitutes a paradigm. The words of the same paradigm have in common their semantic adequacy with the constant parts of the sentence, but they differ according to a system of symmetries or oppositions. A paradigm is thus a system of variations on a background of semantic constants. 

Many words in a language are associated with other words that designate complementary syntactic/semantic roles in a standard way. For example, the grammatical subject of the verb « to steal » is a “thief » and the object of the theft is a “larceny ». When we speak of a vehicle, the person who operates it is a « driver » or « chauffeur ». These systems of matching between words in a language have been particularly studied under the names of lexical functions, collocations, and frames. Dependency relations between word uses – relations that reflect semantic and practical connections – are rightfully part of the conventions of languages and should be systematically included in dictionaries worthy of the name. 

We can also classify under the broad umbrella of paradigms the sets of words that keep their fundamental concept – the lemma is identical – while changing their grammatical class. For example: « metaphor » (a noun that can be used in the role of an actant), « metaphorize » (a verb that is used in the role of an action), « metaphorical » (an adjective that is used to qualify a noun) and « metaphorically » (an adverb that is used to qualify a verb). 

In sum, paradigms correspond to these three cases:

  • they are substitution groups of inflections or grammatical roles for a constant lemma;
  • they are substitution groups of words in a sentence and for a constant grammatical role;
  • finally, they are more or less complex systems of word (or phrase) co-occurrence as in lexical functions, collocations or frames.

Let us remember that each node of a syntagmatic tree belongs to a paradigm, i.e. to a matrix of alternative possibilities relevant in a certain context. A paradigmatic matrix describes a domain of semantic variation structured by a system of symmetries or oppositions. Paradigmatic variables are generally co-dependent: the choice of a word in a syntagmatic role conditions the choice of words in the other roles. In all cases, a paradigm is a field of semantic variations that are appropriate to a given context.

The semiotic axis

Some linguists add to the two syntagmatic and paradigmatic axes a third axis, semiotic, which concerns the relationship between the signifier and the signified or, if one prefers, the relationship between the sound (the signifier) and the meaning (the signified) of linguistic expressions.

Meaning involves at least three actants who play distinct roles. A sign (a) indicates something: the referent (b), for someone: the interpretant (c). The linguistic symbol is a particular type of sign, divided into two parts: the signifier and the signified.

We say that a linguistic symbol is conventional because, in most cases, there is no analogy or causal link between the sound and the concept: for example, between the sound « tree » and a kind of plant. The meaning of the sound « tree » is governed by the English language and is not left to the choice of the interpreter. However, it is in the context of a particular speech act that the interlocutor understands the referent of the word: is it a syntactic tree, a palm tree, a Christmas tree… ? Let us remember this important distinction: the signified is determined by the language but the referent identified by the interpreter depends on the context. We sometimes make the mistake of attributing the connection between the signifier and the signified to the interpreter because natural languages are ambiguous, and the interpreter often uses his or her understanding of the context to determine the signified of an equivocal signifier… But the fundamental intermediary between the signifier and the signified is none other than the linguistic system itself.

Figure 3. The semiotic axis: a signifying chain corresponds to a network of concepts, i.e., a syntagmatic tree crossed by paradigmatic matrices.

It has been noticed for centuries that, except for a few rare cases of words whose sound evokes the meaning (the name « cuckoo » reminds us of the song of the bird), the phonetics of a word has no direct relationship with its semantics. The relationship between the sound and the meaning of words is purely conventional and depends on the language. However, the independence of sound and meaning in speech should not be exaggerated. The more poetic the language, the more phonetic aspects such as rhythms and assonance – especially rhymes – contribute to the creation of meaning. Moreover, deciphering the syntagmatic dimension – that is, reconstructing a dependency tree including identifying the grammatical role of leaves – relies heavily on word order, the use of ear-sensitive cases, punctuation, and tonal accent. It is not a question here of a direct term-to-term correspondence between signifying units and signified units but rather of an analogy or resonance between sound structure and grammatical structure. Finally, phonetics plays a role in the recognition of the paradigmatic dimension, for example when it allows us to identify a constant part and a variable part in a word. Let’s note for example the alternation «muchacho/muchacha» where the semantic constant and the gender variable is easily recognizable. Similarly for the alternation «tart/tartlet»: the semantic constant as well as the size variation are audible. But to designate a mini-mountain, we do not say a «mountainlet» but a hill. Mountain and hill are however part of the same paradigm of topological accidents and geographical descriptions, they have roughly the same shape (foot, slope, summit) while opposing each other on a small/large scale of variation. None of the above, however, is reported at the phonetic level. In this vein of paradigms impossible to recognize by sound, we can evoke colors: green, red, yellow and blue are opposed in the same color paradigm but their belonging to the same paradigm is not phonetically sensitive. If phonetics often helps to encode and decode the syntagmatic axis in natural languages, it only rarely plays this role for the paradigmatic axis.

Let us keep in mind this last point, which will prove to be crucial for the solution of the semantic computation problem because, in IEML – and contrary to the situation that prevails in natural languages – all the words of the same paradigm have a phonetic invariant in common (see the color paradigm in IEML in Table 1 below).

Word paradigms in IEML

Except for conjugations and grammatical cases, natural languages dictionaries don’t organize their words by paradigms, but by alphabetical order (except for Chinese dictionaries that are organized by ideographic « radicals », number of strokes, etc.). For instance, in an English dictionary, there is no paradigm for colours. But such a paradigm of colours exists in the IEML dictionary. Indeed, each word belongs explicitly and exclusively to a unique root-paradigm, generated by one single paradigmatic function. In IEML, the words of the same paradigm have a common phonetic or signifier part. The semantic invariant is represented by a syntactic invariant. Paradigms are represented by one or more tables – or matrices –, whose cells are words.

Sentence paradigms work according to the same principles (A sentence paradigm is a sentence composed of two parts: a constant part and a variable part. The variable part can concern one, two or three, at most, roles). As a consequence, it is easy to select a semantic unit or to explore its semantic relationships when editing a text. When looking at paradigmatic tables, IEML semantic units quickly reveal themselves as nodes in matrixes of relationships. As a first approximation, a paradigm can be defined as the set of internal differences within a semantic field. A paradigm thus represents a range of variations on a common theme. Furthermore, a paradigm may be recursively broken down into sub-paradigms. Not only do all cells in a table have the same theme (colours, size adjectives, verb tenses, etc.) but cells in the same column or row have common sub-themes (red variations among colours, lengths or widths among sizes, different modes among the same tense, etc.). Semantic constants in columns or rows correspond to « algebraic » constants in the semantic unit structure: words in the same row have a common substance and words in the same column have a common attribute.

Table 1 : Colors

The paradigm represented in Table 1 is generated by the function :
« (U:.e.- ⊕ A:.e.- ⊕ S:.e.- ⊕ B:.e.- ⊕ T:.e.-) ⊗ (U:.i.- ⊕ A:.i.- ⊕ S:.i.- ⊕ B:.i.- ⊕ T:.i.-) »The invariant letters e. in the second place and i. in the fourth place are used to identify the color paradigm. The variables U: and A: represent the white and the black while the variables S: B: and T: represent the three primary colors blue, yellow and red. The principal nuances are in substance and the secondary nuances in attribute.

Table 2: Paradigm of Performative Acts

A distinct IEML word belongs to one single paradigm. Formally, a paradigm is a set of words at the same layer which is generated by a semantic function. For example, the Table 2 of performative acts above shows the paradigm resulting from the function O:M:.O:M:.-

  • The input variables, in substance and in attribute (O:M:. = y. + o. + e. + u. + a. + i.) are all vowels from layer 1.
  • The resulting words are all made up of a multiplication of two letters (one in substance and one in attribute).
  • The rows contain the words with an identical substance, the columns shows words with the same attribute and all the words of the paradigm have the same mode (E) that is not represented.

The respective positions of the words on the tables display as much as possible their semantic relations. At a glance, the paradigmatic tables show the words most related to each other, like those on the same row, on the same column or those that appear linked by various symmetric patterns, like an exchange of substance and attribute on the diagonal. An example of the way formal symmetries between words of the same paradigm correspond to semantic symmetries is the relation between y.u.- « to question » and u.y.- « to respond », in the above Table 2 of « performative acts ».

Sentence paradigms in IEML

A sentence paradigm is a sentence composed of two parts: a constant part and a variable part. The variable part can concern one, two or three (at most) roles. Variables are presented as #concepts between braces and separated by a semicolon.

In the example below, role 1 has a substitution group of five variables. « 1d: /#/1 » indicates that the paradigm has only one dimension (one variable role) and that this role is the initiator (role number 1).

fr:paradigme des fonctions psychiques
en:psychic functions paradigm
1d: /#/1
(0 #mental health symptoms,
1 { #psychic autonomy; #subjective dimension; #emotional dimension; #cognitive dimension; #personal memory }

In the context of building a mental health ontology in IEML[1], I have developed Table 3, which organizes the major categories of symptoms in this area. We see that the above paradigm lists the five main rows in Table 3 below.

Table 3: the most general psychological functions in an ontology of mental health

I used the fundamental symmetries of IEML to order the universe of discourse of mental health symptoms. The top row corresponds to the emergent qualities of the psyche in its most virtual dimension (autonomy) while the bottom row corresponds to the most actual dimension, which concretely supports the other psychic functions (memory). Between these two dimensions, the ascending and descending information is coded and decoded on a subjective (sign), emotional (being) and cognitive (thing) mode, as we see in the three intermediate rows. The three columns of the table correspond roughly to a sign / being / thing partition and the binary subdivision within each of the fifteen rectangles corresponds to a division between the most virtual aspects (for the top cell) and the most actual (for the bottom cell).

Note, in the row « subjectivation » that the subject relates to himself in the first box, to the alter ego in the second, and to reality in the third. The « thought » represents the way the subject relates to reality, hence its affinity with the thing. On the other hand, in the third box of the « emotion » row, mood is the emotion felt and affect is the emotion expressed.

To build such a table in IEML, it is sufficient to organize the paradigms by means of a tree structure in which the variables of a higher level (more general) paradigm become the constants of a lower level (more detailed) paradigm. For example, to create the three columns of the fifth row concerning memory, we write the following paradigm.

fr:paradigme des symptômes liés à la mémoire personnelle
en:paradigm of symptoms related to the personal memory
1d: /#/2
0 #mental health symptoms,
1 #personal memory,
2 {#consciousness; #intermediate memory; #long-term memory}

To specify the type of symptoms concerning long-term memory, we write the following paradigm.

fr:paradigme des symptômes liés à la mémoire à long terme
en:paradigm of symptoms related to the long term memory
0 #mental health symptoms,
1 #personal memory,
2 #long-term memory,
4 {#declarative; #non declarative}

A feature of the IEML editor allows to nest sentence paradigms inside each other to create complex paradigm trees and automatically generate tables. For example, the « perceptual problems » cell in the third column of the fourth row of Table 3, in turn, contains the two-dimensional paradigm in Table 4 below.

Table 4

Table 4 is generated by the sentence paradigm below.

fr:paradigme des symptômes liés à la perception
en:paradigm of symptoms related to perception
1d: /#/1
2d: /#/2
0 #perception problems -,
1 {#hypersensitivity; #disability; #pain; #illusions; #hallucinations},
2 {#sense of hearing; #sense of sight; #sense of smell; #sense of taste; #sense of touch; #cenesthesia}

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