Modelling implicit dynamic introduction of function symbols in mathematical texts

ABSTRACT. The specialized language of mathematics has a number of linguistically and logically interesting features. One of them, which to our knowledge has not been systematically studied before, is the implicit dynamic introduction of function symbols, exemplified by constructs of the form "for every x there is an f(x) such that ...". We present an extension of Groenendijk and Stokhof's Dynamic Predicate Logic -- Typed Higher-Order Dynamic Predicate Logic -- which formally models this feature of the language of mathematics. Furthermore, we illustrate how the implicit dynamic introduction of function symbols is treated in the proof checking algorithm of the Naproche system.