Logique mathématique et linguistique formelle
This work addresses foundational issues in logic and linguistics, offering insights for researchers in formal semantics and computational linguistics, but it appears to be a survey or lecture rather than presenting new experimental results.
The paper explores the historical and contemporary relationships between logic and language, focusing on how type theory serves as a framework for natural language syntax and interpretation at various levels, such as words, sentences, and discourse.
As the etymology of the word shows, logic is intimately related to language, as exemplified by the work of philosophers from Antiquity and from the Middle-Age. At the beginning of the XX century, the crisis of the foundations of mathematics invented mathematical logic and imposed logic as a language-based foundation for mathematics. How did the relations between logic and language evolved in this newly defined mathematical framework? After a survey of the history of the relation between logic and linguistics, traditionally focused on semantics, we focus on some present issues: 1) grammar as a deductive system 2) the transformation of the syntactic structure of a sentence to a logical formula representing its meaning 3) taking into account the context when interpreting words. This lecture shows that type theory provides a convenient framework both for natural language syntax and for the interpretation of any of tis level (words, sentences, discourse).