Generating References to Parts of Recursively Structured Objects

Algorithms that generate expressions to identify a referent are mostly tailored towards objects which are in some sense conceived as holistic entities, describing them in terms of their properties and relations to other objects. This approach may prove not fully adequate when referring to components of structured objects, specifically for abstract objects in formal domains, where scope and relative positions are essential features. In this paper, we adapt the standard Dale and Reiter algorithm to specifics of such references as observed in a corpus about mathematical proofs. Extensions incorporated include an incremental specialization of property values for metonymic references, local and global positions reflecting group formations and implicature-based scope preferences to justify unique identification of the intended referent. The approach is primarily relevant for domains where abstract formal objects are prominent, but some of its features are also useful to extend the expressive repertoire of reference generation algorithms in other domains.