Copredication in Homotopy Type Theory

This paper applies homotopy type theory to formal semantics of natural languages and proposes a new model for the linguistic phenomenon of copredication. Copredication refers to sentences where two predicates which assume di erent requirements for their arguments are asserted for one single entity, e.g., “the lunch was delicious but took forever”. This paper is particularly concerned with copredication sentences with quanti cation, i.e., cases where the two predicates impose distinct criteria of quanti cation and individuation, e.g., “Fred picked up and mastered three books.” In our solution developed in homotopy type theory and using the rule of existential closure following Heim analysis of inde nites, common nouns are modeled as identi cations of their aspects using HoTT identity types, e.g., the common noun book is modeled as identi cations of its physical and informational aspects. The previous treatments of copredication in systems of semantics which are based on simple type theory and dependent type theories make the correct predictions but at the expense of ad hoc extensions (e.g., partial functions, dot types and coercive subtyping). The model proposed here, also predicts the correct results but using a conceptually simpler foundation and no ad hoc extensions. The proofs in the proposal have been formalized using Agda.