Interpreting Plurals in the Naproche CNL

The Naproche CNL [2] is a controlled natural language for mathematical texts, i.e. a controlled subset of the semi-formal language of mathematics (SFLM) as used in mathematical journals and textbooks. The Naproche system translates Naproche CNL texts first into Proof Representation Structures (PRSs, [2]), an adapted version of Discourse Representation Structures, which are further translated into lists of first-order formulae which are used for checking the logical correctness of a Naproche text using automated theorem provers. The two main applications that we have in mind for Naproche are to make formal mathematics more readable to the average mathematician, and to use it as a tool that can help undergraduate students to learn how to write formally correct proofs and thus get used to (a subset of) SFML. A recent addition to the Naproche CNL is the possibility to make plural statements. By this we mean not only statements involving nouns in the plural (e.g. “numbers”) and verbs conjugated in plural forms (e.g. “are”), but also conjunctions of noun phrases (e.g. “x + y and x · y are even”). We discuss the collective-distributive ambiguity as well as a special scope ambiguity conjunctions give rise to, and explain how these ambiguities are resolved in Naproche. Plural definite noun phrases (e.g. “the real numbers”) are not yet implemented in Naproche and are left out of the discussion in this abstract.