Alleged assassins: Realist and constructivist semantics for modal modification

Modal modifiers such as Alleged oscillate between being subsective and being privative. If individual a is an alleged assassin (at some parameter of evaluation) then it is an open question whether a is an assassin (at that parameter). Standardly, modal modifiers are negatively defined, in terms of failed inferences or non-intersectivity or non-extensionality. Modal modifiers are in want of a positive definition and a worked-out logical semantics. This paper offers two positive definitions. The realist definition is elaborated within Tichý’s Transparent Intensional Logic (TIL) and builds upon Montague’s model-theoretic semantics for adjectives as representing mappings from properties to properties. The constructivist definition is based on an extension of Martin-Löf’s Constructive Type Theory (CTT) so as to accommodate partial verification. We show that, and why, “a is an alleged assassin” and “Allegedly, a is an assassin” are equivalent in TIL and synonymous in CTT.