Prompt:

"I'm developing a formal and normative framework for understanding idiomatic phrases in natural language. I want to treat the whole phrase - particularly noun phrases - as the primary extant referent, without presupposing internal syntactic structure. The internal parts (like adjectives or determiners) should be treated as synthetic, revealed only through an act of analysis. I'm also interested in defining a special subclass of idioms that are 'commutative,' meaning their syntactic decomposition and semantic interpretation can be reversed to reproduce the original phrase. I want to begin interpretation by assuming possible non-commutative label:referent associations, rather than assuming compositional transparency. Can you help me formalize this framework with clearly defined principles, a typology of idioms, and a philosophical justification for this approach?"