'Grammatical' vs. 'Lexical' Meaning Constructors for Glue Semantics

Current theories of formal semantics allow arguments of predicates to be of non-basic types, such as e→p (e for ‘entity’, p for ‘proposition’, with no commitment to any particular treatment of propositions). ‘Modal adjectives’ such as alleged are for example standardly analysed as being of type (e→p)→(e→p). But such analyses allow certain kinds of modal adjectives that don’t seem to exist, such as a hypothetical alleger, such that an alleger murderer would be somebody who has made allegations that somebody (else) is a murderer. Here I make a proposal using LFG ‘glue semantics’ that permits it to avoid allowing this kind of adjectival meaning, by dividing the basic compositional units of meaning into an open class of ‘lexical meanings’, of strongly restricted form, and a finite class fixed by UG of ‘grammatical meanings’, which don’t obey these restrictions