Towards a Mathematical and Computational Theory of Meaning in Natural Languages.

In one hand, the meaning of natural languages is often described with basic semantic features and a boolean composition of these features. However, this approach is not sufficient to describe more deeply the meaning of linguistic units. In the other hand, the semantic of computer languages often starts from Church’s λ-calculus and walks up to more abstract levels. In this communication, is introduced a new general computational approach of the representation of meanings for high level languages (natural languages and programming languages), in working from the paradigm of compilation in computer sciences. In this compilation paradigm, the expressions of a high level symbolic language are changed in representations by means of intermediary levels, to hit formal representations directly compatible with the material structures of a machine or of a brain. From this analogy, expressions of a natural language can be analyzed by different metalinguistic levels of representations linked to each other by changing representation processes. The communication will give examples of representation changing between expressions of English and representations of meanings expressed by algebra of “treilles”.