Propositions, Questions, and Adjectives: a rich type theoretic approach

We consider how to develop types corresponding to propositions and questions. Starting with the conception of Propositions as Types, we consider two empirical challenges for this doctrine. The first relates to the putative need for a single type encompassing questions and propositions in order to deal with Boolean operations. The second relates to adjectival modification of question and propositional entities. We partly defuse the Boolean challenge by showing that the data actually argue against a single type covering questions and propositions. We show that by analyzing both propositions and questions as records within Type Theory with Records (TTR), we can define Boolean operations over these distinct semantic types. We account for the adjectival challenge by embedding the record types defined to deal with Boolean operations within a theory of semantic frames formulated within TTR.