Functional Language Logic

The formalism of Functional Language Logic (FLL) is presented, which is an extension of a logical formalism already introduced to represent sentences in natural languages. In the FLL framework, a sentence is represented by aggregating primitive predicates corresponding to words of a fixed language (English in the given examples). The FLL formalism constitutes a bridge between mathematical logic (high-order predicate logic) and the classical logical analysis of discourse, rooted in the Western linguistic tradition. Namely, FLL representations reformulate on a rigorous logical basis many fundamental classical concepts (complementation, modification, determination, specification, …), becoming, at the same time, a natural way of introducing mathematical logic through natural language representations, where the logic of linguistic phenomena is analyzed independently from the single syntactical and semantical choices of particular languages. In FLL, twenty logical operators express the mechanisms of logical aggregation underlying meaning constructions. The relevance of FLL in chatbot interaction is considered, and a problem concerning the relationship between embedding vectors in LLM (Large Language Model) transformers and FLL representations is posed.