IEML (the Information Economy Meta Language) has four main directions of research and development in 2019: in mathematics, data science, linguistics and software development. This blog entry reviews them successively.

1- A mathematical research program

I will give here a philosophical description of the structure of IEML, the purpose of the mathematical research to come being to give a formal description and to draw from this formalisation as much useful information as possible on the calculation of relationships, distances, proximities, similarities, analogies, classes and others… as well as on the complexity of these calculations. I had already produced a formalization document in 2015 with the help of Andrew Roczniak, PhD, but this document is now (2019) overtaken by the evolution of the IEML language. The Brazilian physicist Wilson Simeoni Junior has volunteered to lead this research sub-program.

IEML Topos

The “topos” is a structure that was identified by the great mathematician Alexander Grothendieck, who “is considered as the re-founder of algebraic geometry and, as such, as one of the greatest mathematicians of the 20th century” (see Wikipedia).

Without going into technical details, a topos is a bi-directional relationship between, on the one hand, an algebraic structure, usually a “category” (intuitively a group of transformations of transformation groups) and, on the other hand, a spatial structure, which is geometric or topological. 

In IEML, thanks to a normalization of the notation, each expression of the language corresponds to an algebraic variable and only one. Symmetrically, each algebraic variable corresponds to one linguistic expression and only one. 

Topologically, each variable in IEML algebra (i.e. each expression of the language) corresponds to a “point”. But these points are arranged in different nested recursive complexity scales: primitive variables, morphemes of different layers, characters, words, sentences, super-phrases and texts. However, from the level of the morpheme, the internal structure of each point – which comes from the function(s) that generated the point – automatically determines all the semantic relationships that this point has with the other points, and these relationships are modelled as connections. There are obviously a large number of connection types, some very general (is contained in, has an intersection with, has an analogy with…) others more precise (is an instrument of, contradicts X, is logically compatible with, etc.).

The topos that match all the expressions of the IEML language with all the semantic relationships between its expressions is called “The Semantic Sphere”.

Algebraic structure of IEML

In the case of IEML, the algebraic structure is reduced to 

  • 1. Six primitive variables 
  • 2. A non-commutative multiplication with three variables (substance, attribute and mode). The IEML multiplication is isomorphic to the triplet ” departure vertex, arrival vertex, edge ” which is used to describe the graphs.
  • 3. A commutative addition that creates a set of objects.

This algebraic structure is used to construct the following functions and levels of variables…

1. Functions using primitive variables, called “morpheme paradigms”, have as inputs morphemes at layer n and as outputs morphemes at layer n+1. Morpheme paradigms include additions, multiplications, constants and variables and are visually presented in the form of tables in which rows and columns correspond to certain constants.

2. “Character paradigms” are complex additive functions that take morphemes as inputs and characters as outputs. Character paradigms include a group of constant morphemes and several groups of variables. A character is composed of 1 to 5 morphemes arranged in IEML alphabetical order. (Characters may not include more than five morphemes for cognitive management reasons).

3. IEML characters are assembled into words (a substance character, an attribute character, a mode character) by means of a multiplicative function called a “word paradigm”. A word paradigm intersects a series of characters in substance and a series of characters in attribute. The modes are chosen from predefined auxiliary character paradigms, depending on whether the word is a noun, a verb or an auxiliary. Words express subjects, keywords or hashtags. A word can be composed of only one character.

4. Sentence building functions assemble words by means of multiplication and addition, with the necessary constraints to obtain grammatical trees. Mode words describe the grammatical/semantic relationships between substance words (roots) and attribute words (leaves). Sentences express facts, proposals or events; they can take on different pragmatic and logical values.

5. Super-sentences are generated by means of multiplication and addition of sentences, with constraints to obtain grammatical trees. Mode sentences express relationships between substance sentences and attribute sentences. Super-sentences express hypotheses, theories or narratives.

6. A USL (Uniform Semantic Locator) or IEML text is an addition (a set) of words, sentences and super-sentences. 

Topological structure of IEML: a semantic rhizome


The philosophical notion of rhizome (a term borrowed from botany) was developed on a philosophical level by Deleuze and Guattari in the preface to Mille Plateaux (Minuit 1980). In this Deleuzo-Guattarian lineage, by rhizome I mean here a complex graph whose points or “vertices” are organized into several levels of complexity (see the algebraic structure) and whose connections intersect several regular structures such as series, tree, matrix and clique. In particular, it should be noted that some structures of the IEML rhizome combine hierarchical or genealogical relationships (in trees) with transversal or horizontal relationships between “leaves” at the same level, which therefore do not respect the “hierarchical ladder”. 


We can distinguish the abstract, or virtual, rhizomatic grid drawn by the grammar of the language (the sphere to be dug) and the actualisation of points and relationships by the users of the language (the dug sphere of chambers and galleries).  Characters, words, sentences, etc. are all chambers in the centre of a star of paths, and the generating functions establish galleries of “rhizomatic” relationships between them, as many paths for exploring the chambers and their contents. It is therefore the users, by creating their lexicons and using them to index their data, communicate and present themselves, who shape and grow the rhizome…

Depending on whether circuits are more or less used, on the quantity of data or on the strength of interactions, the rhizome undergoes – in addition to its topological transformations – various types of quantitative or metric transformations. 

* The point to remember is that IEML is a language with calculable semantics because it is also an algebra (in the broad sense) and a complex topological space. 

* In the long term, IEML will be able to serve as a semantic coordinate system for the information world at large.

2 A research program in data science

The person in charge of the data science research sub-program is the software engineer (Eng. ENSIMAG, France) Louis van Beurden, who holds also a master’s degree in data science and machine translation from the University of Montréal, Canada. Louis is planning to complete a PhD in computer science in order to test the hypothesis that, from a data science perspective, a semantic metadata system in IEML is more efficient than a semantic metadata system in natural language and phonetic writing. This doctoral research will make it possible to implement phases A and B of the program below and to carry out our first experiment.

Background information

The basic cycle in data science can be schematized according to the following loop:

  • 1. selection of raw data,
  • 2. pre-processing, i.e. cleaning data and metadata imposition (cataloguing and categorization) to facilitate the exploitation of the results by human users,
  • 3. statistical processing,
  • 4. visual and interactive presentation of results,
  • 5. exploitation of the results by human users (interpretation, storytelling) and feedback on steps 1, 2, 3

Biases or poor quality of results may have several causes, but often come from poor pre-treatment. According to the old computer adage “garbage in, garbage out“, it is the professional responsibility of the data-scientists to ensure the quality of the input data and therefore not to neglect the pre-processing phase where this data is organized using metadata.

Two types of metadata can be distinguished: 1) semantic metadata, which describes the content of documents or datasets, and 2) ordinary metadata, which describes authors, creation dates, file types, etc. Let us call “semantic pre-processing” the imposition of semantic metadata on data.


Since IEML is a univocal language and the semantic relationships between morphemes, words, sentences, etc. are mathematically computable, we assume that a semantic metadata system in IEML is more efficient than a semantic metadata system in natural language and phonetic writing. Of course, the efficiency in question is related to a particular task: search, data analysis, knowledge extraction from data, machine learning, etc.

In other words, compared to a “tokenization” of semantic metadata in phonetic writing noting a natural language, a “tokenization” of semantic metadata in IEML would ensure better processing, better presentation of results to the user and better exploitation of results. In addition, semantic metadata in IEML would allow datasets that use different languages, classification systems or ontologies to be de-compartmentalized, merged and compared.

Design of the first experience

The ideal way to do an experiment is to consider a multi-variable system and transform only one of the system variables, all other things being equal. In our case, it is only the semantic metadata system that must vary. This will make it easy to compare the system’s performance with one (phonetic tokens) or the other (semantic tokens) of the semantic metadata systems.

  • – The dataset of our first experience encompasses all the articles of the Sens Public scientific journal.
  • – Our ordinary metadata are the author, publication date, etc.
  • – Our semantic metadata describe the content of articles.
  •     – In phonetic tokens, using RAMEAU categories, keywords and summaries,
  •     – In IEML tokens by translating phonetic tokens.
  • – Our processes are “big data” algorithms traditionally used in natural language processing 
  •     – An algorithm for calculating the co-occurrences of keywords.
  •     – A TF-IDF (Term Frequency / Inverse Document Frequency) algorithm that works from a word / document matrix.
  •     – A clustering algorithm based on “word embeddings” of keywords in articles (documents are represented by vectors, in a space with as many dimensions as words).
  • – A user interface will offer a certain way to access the database. This interface will be obviously adapted to the user’s task (which remains to be chosen, but could be of the “data analytics” type).
  • Result 1 corresponds to the execution of the “machine task”, i.e. the establishment of a connection network on the articles (relationships, proximities, groupings, etc.). We’ll have to compare….
  •     – result 1.1 based on the use of phonetic tokens with 
  •     – result 1.2 based on the use of IEML tokens.
  • Result 2 corresponds to the execution of the selected user-task (data analytics, navigation, search, etc.). We’ll have to compare….
  •     – result 2.1, based on the use of phonetic tokens, with 
  •     – result 2.2, based on the use of IEML tokens.

Step A: First indexing of a database in IEML

Reminder: the data are the articles of the scientific journal, the semantic metadata are the categories, keywords and summaries of the articles. From the categories, keywords and article summaries, a glossary of the knowledge area covered by the journal is created, or a sub-domain if it turns out that the task is too difficult. It should be noted that in 2019 we do not yet have the software tools to create IEML sentences and super-phrases that allow us to express facts, proposals, theories, narratives, hypotheses, etc. Phrases and super-phrases, perhaps accessible in a year or two, will therefore have to wait for a later phase of the research.

The creation of the glossary will be the work of a project community, linked to the editors of Sens-Public magazine and the Canada Research Chair in Digital Writing (led by Prof. Marcello Vitali-Rosati) at the Université de Montréal (Digital Humanities). Pierre Lévy will accompany this community and help it to identify the constants and variables of its lexicon. One of the auxiliary goals of the research is to verify whether motivated communities can appropriate IEML to categorize their data. Once we are satisfied with the IEML indexing of the article database, we will proceed to the next step.

Step B: First experimental test

  • 1. The test is determined to measure the difference between results based on phonetic tokens and results based on IEML tokens. 
  • 2. All data processing operations are carried out on the data.
  • 3. The results (machine tasks and user tasks) are compared with both types of tokens.

The experiment can eventually be repeated iteratively with minor modifications until satisfactory results are achieved.

If the hypothesis is confirmed, we proceed to the next step

Step C: Towards an automation of semantic pre-processing in IEML.

If the superior efficiency of IEML tokens for semantic metadata is demonstrated, then there will be a strong interest in maximizing the automation of IEML semantic pre-processing

The algorithms used in our experiment are themselves powerful tools for data pre-processing, they can be used, according to methods to be developed, to partially automate semantic indexing in IEML. The “word embeddings” will make it possible to study how IEML words are correlated with the natural language lexical statistics of the articles and to detect anomalies. For example, we will check if similar USLs (a USL is an IEML text) point to very different texts or if very different texts have similar USLs. 

Finally, methods will be developed to use deep learning algorithms to automatically index datasets in IEML.

Step D: Research and development perspective in Semantic Machine Learning

If step C provides the expected results, i.e. methods using AI to automate the indexing of data in IEML, then big data indexed in IEML will be available.  As progress will be made, semantic metadata may become increasingly similar to textual data (summary of sections, paragraphs, sentences, etc.) until translation into IEML is achieved, which remains a distant objective.

The data indexed in IEML could then be used to train artificial intelligence algorithms. The hypothesis that machines learn more easily when data is categorized in IEML could easily be validated by experiments of the same type as described above, by comparing the results obtained from training data indexed in IEML and the results obtained from the same data indexed in natural languages.

This last step paves the way for a better integration of statistical AI and symbolic AI (based on facts and rules, which can be expressed in IEML).

3 A research program in linguistics, humanities and social sciences


The semiotic and linguistic development program has two interdependent components:

1. The development of the IEML metalanguage

2. The development of translation systems and bridges between IEML and other sign systems, in particular… 

  •     – natural languages,
  •     – logical formalisms,
  •     – pragmatic “language games” and games in general,
  •     – iconic languages,
  •     – artistic languages, etc.

This research and development agenda, particularly in its linguistic dimension, is important for the digital humanities. Indeed, IEML can serve as a system of semantic coordinates of the cultural universe, thus allowing the humanities to cross a threshold of scientific maturity that would bring their epistemological status closer to that of the natural sciences. Using IEML to index data and to formulate assumptions would result in….

  • (1) a de-silo of databases used by researchers in the social sciences and humanities, which would allow for the sharing and comparison of categorization systems and interpretive assumptions;
  • (2) an improved analysis of data.
  • (3) The ultimate perspective, set out in the article “The Role of the Digital Humanities in the New Political Space” ( in French), is to aim for a reflective collective intelligence of the social sciences and humanities research community. 

But IEML’s research program in the perspective of the digital humanities – as well as its research program in data science – requires a living and dynamic semiotic and linguistic development program, some aspects of which I will outline here.

IEML and the Meaning-Text Theory

IEML’s linguistic research program is very much based on the Meaning-Text theory developed by Igor Melchuk and his school. “The main principle of this theory is to develop formal and descriptive representations of natural languages that can serve as a reliable and convenient basis for the construction of Meaning-Text models, descriptions that can be adapted to all languages, and therefore universal. ”(Excerpt translated from the Wikipedia article on Igor Melchuk). Dictionaries developed by linguists in this field connect words according to universal “lexical functions” identified through the analysis of many languages. These lexical functions have been formally transposed into the very structure of IEML (See the IEML Glossary Creation Guide) so that the IEML dictionary can be organized by the same tools (e.g. Spiderlex) as those of the Meaning-Text Theory research network. Conversely, IEML could be used as a pivot language – or concept description language – *between* the natural language dictionaries developed by the network of researchers skilled in Meaning-Text theory.

Construction of specialized lexicons in the humanities and social sciences

A significant part of the IEML lexicon will be produced by communities having decided to use IEML to mark out their particular areas of knowledge, competence or interaction. Our research in specialized lexicon construction aims to develop the best methods to help expert communities produce IEML lexicons. One of the approaches consists in identifying the “conceptual skeleton” of a domain, namely its main constants in terms of character paradigms and word paradigms. 

The first experimentation of this type of collaborative construction of specialized lexicons by experts will be conducted by Pierre Lévy in collaboration with the editorial team of the Sens Public scientific journal and the Canada Research Chair in Digital Textualities at the University of Montréal (led by Prof. Marcello Vitali-Rosati). Based on a determination of their economic and social importance, other specialized glossaries can be constructed, for example on the theme of professional skills, e-learning resources, public health prevention, etc.

Ultimately, the “digital humanities” branch of IEML will need to collaboratively develop a conceptual lexicon of the humanities to be used for the indexation of books and articles, but also chapters, sections and comments in documents. The same glossary should also facilitate data navigation and analysis. There is a whole program of development in digital library science here. I would particularly like to focus on the human sciences because the natural sciences have already developed a formal vocabulary that is already consensual.

Construction of logical, pragmatic and narrative character-tools

When we’ll have a sentence and super-phrase editor, it is planned to establish a correspondence between IEML – on the one hand – and propositional calculus and first order logics – on the other hand –. This will be done by specifying special character-tools to implement logical functions. Particular attention will be paid to formalizing the definition of rules and the declaration that “facts” are true in IEML. It should be noted in passing that, in IEML, grammatical expressions represent classes, sets or categories, but that logical individuals (proper names, numbers, etc.) or instances of classes are represented by “literals” expressed in ordinary characters (phonetic alphabets, Chinese characters, Arabic numbers, URLs, etc.).

In anticipation of practical use in communication, games, commerce, law (smart contracts), chatbots, robots, the Internet of Things, etc., we will develop a range of character-tools with illocutionary force such as “I offer”, “I buy”, “I quote”, “I give an instruction”, etc.

Finally, we will making it easier for authors of super-sentences by developing a range of character-tools implementing “narrative functions”.

4 A software development program

A software environment for the development and public use of the IEML language

Logically, the first multi-user IEML application will be dedicated to the development of the language itself. This application is composed of the following three web modules.

  • 1. A morpheme editor that also allows you to navigate in the morphemes database, or “dictionary”.
  • 2. A character and word editor that also allows navigation in the “lexicon”.
  • 3. A navigation and reading tool in the IEML library as a whole, or “IEML database” that brings together the dictionary and lexicon, with translations, synonyms and comments in French and English for the moment.

The IEML database is a “Git” database and is currently hosted by GitHub. Indeed, a Git database makes it possible to record successive versions of the language, as well as to monitor and model its growth. It also allows large-scale collaboration among teams capable of developing specific branches of the lexicon independently and then integrating them into the main branch after discussion, as is done in the collaborative development of large software projects. As soon as a sub-lexicon is integrated into the main branch of the Git database, it becomes a “common” usable by everyone (according to the latest General Public License version.

Morpheme and word editors are actually “Git clients” that feed the IEML database. A first version of this collaborative read-write environment should be available in the fall of 2019 and then tested by real users: the editors of the Scientific Journal “Sens Public” as well as other participants in the University of Montréal’s IEML seminar.

The following versions of the IEML read/write environment should allow the editing of sentences and texts as well as literals that are logical individuals not translated into IEML, such as proper names, numbers, URLs, etc.

A social medium for collaborative knowledge management

A large number of applications using IEML can be considered, both commercial and non-commercial. Among all these applications, one of them seems to be particularly aligned with the public interest: a social medium dedicated to collaborative knowledge and skills management. This new “place of knowledge” could allow the online convergence of the missions of… 

  • – museums and libraries, 
  • – schools and universities, 
  • – companies and administrations (with regard to their knowledge creation and management dimension), 
  • – smart cities, employment agencies, civil society networks, NGO, associations, etc.

According to its general philosophy, such a social medium should…

  • – be supported by an intrinsically distributed platform, 
  • – have the simplicity – or the economy of means – of Twitter,
  • – ensure the sovereignty of users over their data,
  • – promote collaborative processes.

The main functions performed by this social medium would be:

  • – data curation (reference and categorization of web pages, edition of resource collections), 
  • – teaching offers and learning demands,
  • – offers and demands for skills, or employment market.

IEML would serve as a common language for

  • – data categorization, 
  • – description of the knowledge and skills, 
  • – the expression of acts within the social medium (supply, demand, consent, publish, etc.)
  • – addressing users through their knowledge and skills.

Three levels of meaning would thus be formalized in this medium.

  • (1) The linguistic level in IEML  – including lexical and narrative functions – formalizes what is spoken about (lexicon) and what is said (sentences and super-phrases).
  • – (2) The logical – or referential – level adds to the linguistic level… 
  •     – logical functions (first order logic and propositional logic) expressed in IEML using logical character-tools,
  •     – the ability of pointing to references (literals, document URLs, datasets, etc.),
  •     – the means to express facts and rules in IEML and thus to feed inference engines.
  • – (3) The pragmatic level adds illocutionary functions and users to the linguistic and logical levels.
  •     – Illocutionary functions (thanks to pragmatic character-tools) allow the expression of conventional acts and rules (such as “game” rules). 
  •     – The pragmatic level obviously requires the consideration of players or users, as well as user groups.
  •     – It should be noted that there is no formal difference between logical inference and pragmatic inference but only a difference in use, one aiming at the truth of propositions according to referred states of things, the other calculating the rights, obligations, gains, etc. of users according to their actions and the rules of the games they play.

The semantic profiles of users and datasets will be arranged according to the three levels that have just been explained. The “place of knowledge” could be enhanced by the use of tokens or crypto-currencies to reward participation in collective intelligence. If successful, this type of medium could be generalized to other areas such as health, democratic governance, trade, etc.