Noematic Representation of Sentences: A Logical Formalism for Natural Language Semantics

Functional Language Logic (FLL) is a formalism, in the tradition of Church--Russell type theory, for representing the logical structure underlying natural language. Sentences are decomposed into \emph{noematic formulas}: aggregates of predications built from lemmas and grammatical markers (grammemes) of a fixed language, treated as unary (monoargumental) predicates or as operators over such predicates. This note presents the current form of FLL, where some important points were updated, especially in the formalization of descriptive terms (including quantifiers). An explicit type system is given for the twenty FLL operators, built over a small set of base types, together with a formal grammar, a parser and a type-checker. Cross-linguistic evidence is discussed within a wide spectrum of languages, claiming that surface grammatical diversity is largely a matter of grammaticalization versus lexicalization of noematic substrata. A catalog of semantic equivalences is presented, relating distinct noematic renderings of the same content, together with specific examples. An \textit{abstract syntax} layer between noematic formula and surface sentence is developed, built from three interacting mechanisms (aggregation, grammatical marking, and an anaphora/tag mechanism). A brief report is presented on a prototype Python implementation of the FLL formalism, which consists of a converter from noematic formulae to abstract syntax, a type-checker, a parser, and translators between Python and FLL notations.