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 different 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 quantification, i.e., cases where the two predicates impose distinct criteria of quantification 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 indefinites, common nouns are modeled as identifications of their aspects using HoTT identity types, e.g., the common noun book is modeled as identifications 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.
Copredication in homotopy type theory (PDF Download Available). Available from: https://www.researchgate.net/publication/320704539_Copredication_in_homotopy_type_theory [accessed Oct 30 2017].
Copredication in Homotopy Type Theory: A homotopical approach to formal semantics of natural language
Copredication in Homotopy Type
Indiana University Bloomington
Presentation based on a joint work with Narges
Nematollahi2 and Amr Sabry3
1 Department of Computer Science
2 Department of Linguistics
3 Department of Computer Science
the phenomenon where two or more predicates
with different requirements on their arguments
are applied to a single argument
a) The lunch was delicious but took forever.
b) The heavy book is easy to understand.
c) John picked up and mastered three books.
Asher(2011), nouns as “dot objects”(Pustejovsky,1995)
◦ i.e., objects that can be viewed under different “aspects”
◦ nouns as functions from “records” to “record types”
Luo (2012), Chatzikyriakidisand Luo (2012, 2013, 2015)
◦ common nouns as types
◦ dot types + coercive subtyping
◦ `book' denotes the set of composite objects physical+informational
◦ criteria of individuation are combined during semantic composition
Homotopy Type Theory
intensional version of Martin-Löf’s type theory [ML75]
a proof-relevant interpretation of equality
a full cumulative hierarchy of universes
judgmental vs propositional equality
◦ “=” vs “ ”≡