Reasoning about functionality of core matching functions for information retrieval

Traditional benchmarking methods for information retrieval (IR) are based on experimental performance evaluation^[1-14]. Although the metrics precision and recall can measure the effectiveness of a system, it cannot assess the underlying model. Recently, a theory of "aboutness" has been used for functional benchmarking of IR. Latest research shows the functionality of an IR model is largely determined by its retrieval mechanism, i.e., the matching function. In particular, containment and overlapping (either with or without a threshold value) are the core IR matching functions. The objective of this paper is to model the containment and overlapping matching functions using an aboutness-based framework and analyze them from an abstract and theoretical viewpoint. Separate aboutness relations for containment, pure-overlapping (i.e., without threshold) and threshold-overlapping matching functions are defined, and the sets of properties supported by them are derived and analyzed respectively. These three relations can be used to determine and explain the functionality of an IR system and how the functionality affects the performance of the system. Moreover, they can provide the design guidelines for new IR systems.